Two shapes are worth knowing on sight: one over a sum of squares gives an inverse tangent, and one over the root of a difference of squares gives an inverse sine. One over x times the root of x squared minus a squared gives an inverse secant. Everything else is getting the constants out front.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
This is one over a squared plus x squared, with a equal to 3.
That integrates to one over a, times inverse tangent of x over a.
So it is a third of inverse tangent of x over 3.
The answer is 31tan−1(3x)+C.
Where students go wrong
Losing the one over a. The x over a inside is easy to remember; the matching one over a in front comes from the substitution and is what most of the lost marks are.
Also called arctan integral, arcsin integral, integrals giving inverse trig or a squared plus x squared.
What you can put on this worksheet
Inverse trig forms
∫25+x25dx→ tan−1(5x)+C
Completing the square, and exact pi answers
∫0336−x23dx→ 2π
The arcsecant, u a power of x, and u = cos x or ln x
∫9+x63x2dx→ 31tan−1(3x3)+C
Questions about these worksheets
Yes. Every inverse trig integrals 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 inverse trig integrals 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 3: inverse trig forms, completing the square, and exact pi answers and the arcsecant, u a power of x, and u = cos x or ln x. Tick as many as you want and set how many of each, or let it spread them evenly.
Losing the one over a. The x over a inside is easy to remember; the matching one over a in front comes from the substitution and is what most of the lost marks are.