What is the integral of int ( 1 / (25 + x^2) ) dx ?

1 Answer
Apr 4, 2016

int(1/(25+x^2))dx=1/5 tan^-1 (x/5) +C

Explanation:

int(1/(25+x^2))dx

dx/d(theta)=5tantheta

dx= 5sec^2theta *(d)theta

int(1/(25+25tan^2theta))* 5sec^2theta*(d)theta

int(1/(25(1+tan^2theta)))* 5sec^2theta*(d)theta

1+tantheta=sec^2theta

int(1/(25(sec^2theta)))* 5sec^2theta*(d)theta

int(1/5)*(d)theta+C

x=5tantheta
x/5 = tantheta
tan^-1(x/5)=theta

Plug in:

=1/5 tan^-1 (x/5) +C