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Question

Question: The value of \(e^{\log(\cos x)} + c\) is....

The value of elog⁡(cos⁡x)+ce^{\log(\cos x)} + c is.

A

∫exlog⁡a. 6muex 6mudx\int_{}^{}{e^{x\log a}.\mspace{6mu} e^{x}\mspace{6mu} dx}

B

(ae)x+c(ae)^{x} + c

C

(ae)xlog⁡(ae)+c\frac{(ae)^{x}}{\log(ae)} + c

D

ex1+log⁡a+c\frac{e^{x}}{1 + \log a} + c

Answer

(ae)x+c(ae)^{x} + c

Explanation

Solution

We have, ∫tan⁡−1(2x1−x2) 6mudx\int_{}^{}{\tan^{- 1}\left( \frac{2x}{1 - x^{2}} \right)\mspace{6mu} dx} or ∫x3cos⁡x2 6mudx\int_{}^{}{x^{3}\cos x^{2}\mspace{6mu} dx}

∫tan⁡xsec⁡2x1−tan⁡2x⥂ 6mudx=\int_{}^{}{\tan x}\sec^{2}x\sqrt{1 - \tan^{2}x} ⥂ \mspace{6mu} dx = ⇒ −13(1−tan⁡2x)3/2+c- \frac{1}{3}(1 - \tan^{2}x)^{3/2} + c.