$\int x^x(1+\log x) dx$ is equal to :

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Home Questions CT8B7XXJ38

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int x^x(1+\log x) dx$ is equal to :

Options:

$x^x-c$

$x^x+c$

$x \log x+c$

None of these

Correct Answer:

$x^x+c$

Explanation:

Let $I=\int x^x(1+\ln x) dx$

Let $x^{x}=t \Rightarrow x \ln x=\ln t$

$\Rightarrow\left(x . \frac{1}{x}+\ln x . 1\right)=\frac{1}{t} \frac{d t}{d x}$

$\Rightarrow dx(1+\ln x) x^{x}=dt$

∴ $I=\int d t \Rightarrow I=t+c$

$I=x^{x}+c$

Hence (2) is the correct answer.