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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Indefinite Integration

JEE Main · Mathematics · Indefinite Integration

∫ x x d x is equal to

\int x \log x d x

is equal to

Options

A $\frac{x^{2}}{4}(2 \log x-1)+c$
B $\frac{x^{2}}{2}(2 \log x-1)+c$
C $\frac{x^{2}}{4}(2 \log x+1)+c$
D $\frac{x^{2}}{2}(2 \log x+1)$

Correct answer

A. $\frac{x^{2}}{4}(2 \log x-1)+c$

Step-by-step solution

\begin{aligned} \int \frac{x}{\Pi} \log _{I} x d x &=\log x \cdot \frac{x^{2}}{2}-\int \frac{1}{x} \cdot \frac{x^{2}}{2} d x \\ &=\frac{x^{2}}{2} \log x-\frac{1}{2} \frac{x^{2}}{2}+c \\ &=\frac{x^{2}}{4}(2 \log x-1)+c \end{aligned}

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