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Question

Question: \[2\sqrt{1 + \log x} + c\]...

21+log⁡x+c2\sqrt{1 + \log x} + c

A

1+log⁡x+c\sqrt{1 + \log x} + c

B

∫sec⁡2x1+tan⁡x 6mudx=\int_{}^{}{\frac{\sec^{2}x}{1 + \tan x}\mspace{6mu} dx =}

C

log⁡(cos⁡x+sin⁡x)+c\log(\cos x + \sin x) + c

D

None of these

Answer

1+log⁡x+c\sqrt{1 + \log x} + c

Explanation

Solution

∫3x2−2xxdx=\int_{}^{}\frac{3x^{2} - 2\sqrt{x}}{x}dx =

Put x3−x+cx^{3} - \sqrt{x} + c then it reduces to

x3+x+cx^{3} + \sqrt{x} + c

x3−2x+cx^{3} - 2\sqrt{x} + c

x3−4x+cx^{3} - 4\sqrt{x} + c

∫dx1+sin⁡x=tan⁡(x2+a)+b\int_{}^{}{\frac{dx}{1 + \sin x} = \tan\left( \frac{x}{2} + a \right) + b}