How to integrate 1/(64x^2+100)?

1 Answer
Jrab · Ananda Dasgupta
May 22, 2018

#1/80arctan((4x)/5)+c#

Explanation:

The integral is #int(dx)/(64x^2+100)#

divide the denominator by 64; #1/64intdx/(x^2+(25/16)#

simplify; #1/64intdx/(x^2+(5/4)^2#

use the formula #intdx/(a^2+x^2)=1/aarctan(x/a)+c#

plug in #(1/80)arctan((4x)/5) + c#

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