Solution Found!
Evaluate the following integrals.
Chapter 4, Problem 33E(choose chapter or problem)
Evaluate the following integrals.
\(\int \frac{x^{2}}{\left(25+x^{2}\right)^{2}} d x\)
Questions & Answers
QUESTION:
Evaluate the following integrals.
\(\int \frac{x^{2}}{\left(25+x^{2}\right)^{2}} d x\)
ANSWER:Problem 33E
Evaluate the following integrals.
dx
Answer;
Step 1
The given integral is dx
By the substitution method we can evaluate the limit .
For our convenience let , us take x = 5 tan(p) (or) x = 5 cot(p)
Let , x = 5 tan(p) , that implies = tan(p) =
, sin(p)=
=
and
= cos(p) =
,…………..(1)
Then the integrand becomes =
= , since
= 25.
=