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Question

Question: \[{logsin}x + c\]...

logsinx+c{logsin}x + c

A

logsecx+c{logsec}x + c

B

∫1x4 6mudx\int_{}^{}{\frac{1}{x^{4}}\mspace{6mu} dx}

C

1−3x3+c\frac{1}{- 3x^{3}} + c

D

13x3+c\frac{1}{3x^{3}} + c

Answer

1−3x3+c\frac{1}{- 3x^{3}} + c

Explanation

Solution

−2cos⁡x+c- 2\cos\sqrt{x} + c

12cos⁡x+c2cos⁡x+c\frac{1}{2}\cos\sqrt{x} + c2\cos\sqrt{x} + c

⇒I=−∫tan⁡2xdx\Rightarrow I = - \int \tan ^ { 2 } x d x tan⁡(ex)−x+c\tan(e^{x}) - x + c

⇒I=−∫sec⁡2xdx+∫1dx\Rightarrow I = - \int \sec ^ { 2 } x d x + \int 1 d x sec⁡(ex)+c\sec(e^{x}) + c

⇒ tan⁡(ex)−ex+c\tan(e^{x}) - e^{x} + c