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Question

Question: \(\sqrt{1 + x^{2}} + c\)...

1+x2+c\sqrt{1 + x^{2}} + c

A

3(1+x2)3/2+c3(1 + x^{2})^{3/2} + c

B

13(1+x2)3/2+c\frac{1}{3}(1 + x^{2})^{3/2} + c

C

∫ex(x+1)cos⁡2(xex)dx=\int_{}^{}{\frac{e^{x}(x + 1)}{\cos^{2}(xe^{x})}dx =}

D

tan⁡(xex)+c\tan(xe^{x}) + c

Answer

∫ex(x+1)cos⁡2(xex)dx=\int_{}^{}{\frac{e^{x}(x + 1)}{\cos^{2}(xe^{x})}dx =}

Explanation

Solution

Put sec⁡x+tan⁡x−x+c\sec x + \tan x - x + c

∫sec⁡2x1+tan⁡xdx=∫1tdt=log⁡t+c\int \frac { \sec ^ { 2 } x } { 1 + \tan x } d x = \int \frac { 1 } { t } d t = \log t + c sec⁡x+tan⁡x+x+c\sec x + \tan x + x + c