- #1

mcastillo356

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- TL;DR Summary
- I have a list of elementary integrals, and among them one that involves arctangent; the example I am dealing with is a combination I will propose in the next discussion paragraph.

Hi, PF

1-The elementary integral is ##\displaystyle\int{\displaystyle\frac{1}{a^2+x^2}dx}=\displaystyle\frac{1}{a}\tan^{-1}\displaystyle\frac{x}{a}+C##

2-The example is ##\displaystyle\int{\Big(5x^{3/5}-\displaystyle\frac{3}{2+x^2}\Big)dx}=\displaystyle\frac{25}{8}x^{8/5}-\displaystyle\frac{3}{\sqrt{2}}\tan^{-1}\displaystyle\frac{x}{\sqrt{2}}+C##

The question is: does the first statement agree with the solution showed?; any comment?

Greetings!

PD: I post without preview.

1-The elementary integral is ##\displaystyle\int{\displaystyle\frac{1}{a^2+x^2}dx}=\displaystyle\frac{1}{a}\tan^{-1}\displaystyle\frac{x}{a}+C##

2-The example is ##\displaystyle\int{\Big(5x^{3/5}-\displaystyle\frac{3}{2+x^2}\Big)dx}=\displaystyle\frac{25}{8}x^{8/5}-\displaystyle\frac{3}{\sqrt{2}}\tan^{-1}\displaystyle\frac{x}{\sqrt{2}}+C##

The question is: does the first statement agree with the solution showed?; any comment?

Greetings!

PD: I post without preview.