Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$I=\int \frac{\left(10 x^9+10^x \log _e 10\right)}{\left(x^{10}+10^x\right)} d x$ is equal to :

Options:

$10^x+x^{10}+c$

$10^x-x^{10}+c$

$10^x+x^{10}+c$

$\log _e\left(10^x+x^{10}\right)+c$

Correct Answer:

$\log _e\left(10^x+x^{10}\right)+c$

Explanation:

If $10^x+x^{10}=p \Rightarrow\left(10^x \ln 10+10 x^9\right) d x=d p ; I=\ln \left(x^{10}+10^x\right)+c$

Hence (4) is the correct answer.