Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:
What is $\int \frac{x^4}{1+x^{10}}$
Options:
$\tan^{-1}x^3+C$
$1/5\sin^{-1}x^5+C$
$1/5\tan^{-1}x^5+C$
$\tan^5x+C$
Correct Answer:
$1/5\tan^{-1}x^5+C$
Explanation:
Put $x^5=t$. Then the integral becomes $\int \frac{1}{5(1+t^2)}dt=1/5tan^{-1}t+C=1/5tan^{-1}x^5+C$