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Question: \[\frac{1}{3}\sin^{- 1}x^{3} + c\]...

13sin⁡−1x3+c\frac{1}{3}\sin^{- 1}x^{3} + c

A

∫cos⁡x4−sin⁡2x 6mudx=\int_{}^{}{\cos x\sqrt{4 - \sin^{2}x}}\mspace{6mu} dx =

B

12sin⁡x4−sin⁡2x−2sin⁡−1(12sin⁡x)+c\frac{1}{2}\sin x\sqrt{4 - \sin^{2}x} - 2\sin^{- 1}\left( \frac{1}{2}\sin x \right) + c

C

12sin⁡x4−sin⁡2x+2sin⁡−1(12sin⁡x)+c\frac{1}{2}\sin x\sqrt{4 - \sin^{2}x} + 2\sin^{- 1}\left( \frac{1}{2}\sin x \right) + c

D

12sin⁡x4−sin⁡2x+sin⁡−1(12sin⁡x)+c\frac{1}{2}\sin x\sqrt{4 - \sin^{2}x} + \sin^{- 1}\left( \frac{1}{2}\sin x \right) + c

Answer

∫cos⁡x4−sin⁡2x 6mudx=\int_{}^{}{\cos x\sqrt{4 - \sin^{2}x}}\mspace{6mu} dx =

Explanation

Solution

∫x2+x−6(x−2)(x−1)dx=\int_{}^{}{\frac{x^{2} + x - 6}{(x - 2)(x - 1)}dx =}

Put x+2log⁡(x−1)+cx + 2\log(x - 1) + c then it reduces to

2x+2log⁡(x−1)+c2x + 2\log(x - 1) + c