Integrating trig functions worksheet

Each one is a derivative rule read the other way round: sine integrates to minus cosine, cosine to sine, and sec squared to tan. A multiple inside, like the 3 in sin 3x, divides the answer. Powers of sine and cosine are a different skill, on the trigonometric integrals sheet.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Integrating Trig Functions Date Period Evaluate each integral. $\int 6 \cos 4 x d x$ $\int - 3 \csc^{2} 2 x d x$ $\int - \sin 3 x d x$ $\int - 10 \csc^{2} 5 x d x$ $\int (- 3 \sin x - 3 \cos x) d x$ $\int 2 \sec^{2} 5 x d x$ $\int 3 \sin 5 x d x$ $\int - 4 \csc 5 x \cot 5 x d x$ $\int (7 \sin x + 8 \cos x) d x$ $\int - 11 \csc 2 x \cot 2 x d x$ $\int (9 \sin x + 2 \cos x) d x$ $\int - 5 \sec 3 x \tan 3 x d x$ $\int \sin 4 x d x$ $\int - 2 \csc 6 x \cot 6 x d x$ $\int (- 2 \sin x + 5 \cos x) d x$ $\int - \csc^{2} 2 x d x$ $\int (2 \sin x + 5 \cos x) d x$ $\int - 12 \sec^{2} 5 x d x$ $\int (- 2 \sin x - 9 \cos x) d x$ $\int 2 \csc^{2} 5 x d x$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Integrating Trig Functions

Date Period

Evaluate each integral.

$\int 6 \cos 4 x d x$
$\int - 3 \csc^{2} 2 x d x$
$\int - \sin 3 x d x$
$\int - 10 \csc^{2} 5 x d x$
$\int (- 3 \sin x - 3 \cos x) d x$
$\int 2 \sec^{2} 5 x d x$
$\int 3 \sin 5 x d x$
$\int - 4 \csc 5 x \cot 5 x d x$
$\int (7 \sin x + 8 \cos x) d x$
$\int - 11 \csc 2 x \cot 2 x d x$
$\int (9 \sin x + 2 \cos x) d x$
$\int - 5 \sec 3 x \tan 3 x d x$
$\int \sin 4 x d x$
$\int - 2 \csc 6 x \cot 6 x d x$
$\int (- 2 \sin x + 5 \cos x) d x$
$\int - \csc^{2} 2 x d x$
$\int (2 \sin x + 5 \cos x) d x$
$\int - 12 \sec^{2} 5 x d x$
$\int (- 2 \sin x - 9 \cos x) d x$
$\int 2 \csc^{2} 5 x d x$



Sigma Prep · sigmaprep.io/worksheets Name Integrating Trig FunctionsAnswer keyVersion 1 Date Period Evaluate each integral. $\int 6 \cos 4 x d x$ $\frac{3}{2} \sin 4 x + C$ $\int - 3 \csc^{2} 2 x d x$ $\frac{3}{2} \cot 2 x + C$ $\int - \sin 3 x d x$ $\frac{1}{3} \cos 3 x + C$ $\int - 10 \csc^{2} 5 x d x$ $2 \cot 5 x + C$ $\int (- 3 \sin x - 3 \cos x) d x$ $3 \cos x - 3 \sin x + C$ $\int 2 \sec^{2} 5 x d x$ $\frac{2}{5} \tan 5 x + C$ $\int 3 \sin 5 x d x$ $- \frac{3}{5} \cos 5 x + C$ $\int - 4 \csc 5 x \cot 5 x d x$ $\frac{4}{5} \csc 5 x + C$ $\int (7 \sin x + 8 \cos x) d x$ $- 7 \cos x + 8 \sin x + C$ $\int - 11 \csc 2 x \cot 2 x d x$ $\frac{11}{2} \csc 2 x + C$ $\int (9 \sin x + 2 \cos x) d x$ $- 9 \cos x + 2 \sin x + C$ $\int - 5 \sec 3 x \tan 3 x d x$ $- \frac{5}{3} \sec 3 x + C$ $\int \sin 4 x d x$ $- \frac{1}{4} \cos 4 x + C$ $\int - 2 \csc 6 x \cot 6 x d x$ $\frac{1}{3} \csc 6 x + C$ $\int (- 2 \sin x + 5 \cos x) d x$ $2 \cos x + 5 \sin x + C$ $\int - \csc^{2} 2 x d x$ $\frac{1}{2} \cot 2 x + C$ $\int (2 \sin x + 5 \cos x) d x$ $- 2 \cos x + 5 \sin x + C$ $\int - 12 \sec^{2} 5 x d x$ $- \frac{12}{5} \tan 5 x + C$ $\int (- 2 \sin x - 9 \cos x) d x$ $2 \cos x - 9 \sin x + C$ $\int 2 \csc^{2} 5 x d x$ $- \frac{2}{5} \cot 5 x + C$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Integrating Trig FunctionsAnswer keyVersion 1

Date Period

Evaluate each integral.

$\int 6 \cos 4 x d x$ $\frac{3}{2} \sin 4 x + C$
$\int - 3 \csc^{2} 2 x d x$ $\frac{3}{2} \cot 2 x + C$
$\int - \sin 3 x d x$ $\frac{1}{3} \cos 3 x + C$
$\int - 10 \csc^{2} 5 x d x$ $2 \cot 5 x + C$
$\int (- 3 \sin x - 3 \cos x) d x$ $3 \cos x - 3 \sin x + C$
$\int 2 \sec^{2} 5 x d x$ $\frac{2}{5} \tan 5 x + C$
$\int 3 \sin 5 x d x$ $- \frac{3}{5} \cos 5 x + C$
$\int - 4 \csc 5 x \cot 5 x d x$ $\frac{4}{5} \csc 5 x + C$
$\int (7 \sin x + 8 \cos x) d x$ $- 7 \cos x + 8 \sin x + C$
$\int - 11 \csc 2 x \cot 2 x d x$ $\frac{11}{2} \csc 2 x + C$
$\int (9 \sin x + 2 \cos x) d x$ $- 9 \cos x + 2 \sin x + C$
$\int - 5 \sec 3 x \tan 3 x d x$ $- \frac{5}{3} \sec 3 x + C$
$\int \sin 4 x d x$ $- \frac{1}{4} \cos 4 x + C$
$\int - 2 \csc 6 x \cot 6 x d x$ $\frac{1}{3} \csc 6 x + C$
$\int (- 2 \sin x + 5 \cos x) d x$ $2 \cos x + 5 \sin x + C$
$\int - \csc^{2} 2 x d x$ $\frac{1}{2} \cot 2 x + C$
$\int (2 \sin x + 5 \cos x) d x$ $- 2 \cos x + 5 \sin x + C$
$\int - 12 \sec^{2} 5 x d x$ $- \frac{12}{5} \tan 5 x + C$
$\int (- 2 \sin x - 9 \cos x) d x$ $2 \cos x - 9 \sin x + C$
$\int 2 \csc^{2} 5 x d x$ $- \frac{2}{5} \cot 5 x + C$

How to do these

$\int 6 \cos 2 x d x$

Cosine integrates to sine.
Divide by the 2 from inside.
Six over two is three.

The answer is $3 \sin 2 x + C$ .

Where students go wrong

The sign on sine. The derivative of cos x is minus sin x, so the integral of sin x is minus cos x, not cos x.

Also called integral of sin x, integral of cos x or basic trig integrals.

What you can put on this worksheet

Sine and cosine: $\int 14 \cos 2 x d x$ → $7 \sin 2 x + C$
sec squared, csc squared, sec tan and csc cot: $\int 7 \sec x \tan x d x$ → $7 \sec x + C$

Questions about these worksheets

Yes. Every integrating trig functions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the integrating trig functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: sine and cosine and sec squared, csc squared, sec tan and csc cot. Tick as many as you want and set how many of each, or let it spread them evenly.

The sign on sine. The derivative of cos x is minus sin x, so the integral of sin x is minus cos x, not cos x.

Integrating trig functions worksheet

Select your difficulty

Integrating Trig Functions

Integrating Trig FunctionsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

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