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Question

Question: \[\int_{}^{}\frac{(1 + \log x)^{2}}{x}\mspace{6mu} dx =\]...

∫(1+log⁡x)2x 6mudx=\int_{}^{}\frac{(1 + \log x)^{2}}{x}\mspace{6mu} dx =

A

(1+log⁡x)3+c(1 + \log x)^{3} + c

B

3(1+log⁡x)3+c3(1 + \log x)^{3} + c

C

13(1+log⁡x)3+c\frac{1}{3}(1 + \log x)^{3} + c

D

∫sec⁡pxtan⁡x 6mudx=\int_{}^{}{\sec^{p}x\tan x\mspace{6mu} dx =}

Answer

3(1+log⁡x)3+c3(1 + \log x)^{3} + c

Explanation

Solution

Put −cot⁡x−x+c- \cot x - x + c then

∫(sec⁡x+tan⁡x)2dx=\int_{}^{}{(\sec x + \tan x)^{2}dx =}