∫ 3 x l o g x dx is equal to, 3 1 ( lo g x ) 2 + C, 3 2 ( lo g x ) 2 + C, 3 2 ( lo g x ) 2 + C, 3 1 ( lo g x ) 2 + C

Hints : x = t 2 ⇒ ∫ 3 t 2 ℓ nt ( 2 tdt ) = 3 2 ∫ t ℓ nt dt = 3 2 2 ( ℓ nt ) 2 + c = 3 ( l n x ) 2 + c

∫ 3 x l o g x dx is equal to

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Question: Answered & Verified by Expert

$\int \frac{\log \sqrt{\mathrm{x}}}{3 \mathrm{x}} \mathrm{dx}$ is equal to

MathematicsIndefinite IntegrationWBJEEWBJEE 2010

Options:

A $\frac{1}{3}(\log \sqrt{\mathrm{x}})^2+\mathrm{C}$
B $\frac{2}{3}(\log \sqrt{\mathrm{x}})^2+\mathrm{C}$
C $\frac{2}{3}(\log x)^2+C$
D $\frac{1}{3}(\log x)^2+C$

Solution:

2517 Upvotes Verified Answer

The correct answer is: $\frac{1}{3}(\log \sqrt{\mathrm{x}})^2+\mathrm{C}$

Hints : $\mathrm{x}=\mathrm{t}^2 \Rightarrow \int \frac{\ell \mathrm{nt}}{3 \mathrm{t}^2}(2 \mathrm{tdt})=\frac{2}{3} \int \frac{\ell \mathrm{nt}}{\mathrm{t}} \mathrm{dt}=\frac{2}{3} \frac{(\ell \mathrm{nt})^2}{2}+\mathrm{c}=\frac{(\ln \sqrt{\mathrm{x}})^2}{3}+\mathrm{c}$

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