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Question: \(\int_{}^{}\frac{1 + x + \sqrt{x + x^{2}}}{\sqrt{x} + \sqrt{1 + x}}\) dx is equal to –...

∫1+x+x+x2x+1+x\int_{}^{}\frac{1 + x + \sqrt{x + x^{2}}}{\sqrt{x} + \sqrt{1 + x}} dx is equal to –

A

12\frac { 1 } { 2 } 1+x\sqrt{1 + x} + C

B

23\frac{2}{3} (1 + x)3/2 + C

C

1+x\sqrt{1 + x} + C

D

2(1 + x)3/2 + C

Answer

23\frac{2}{3} (1 + x)3/2 + C

Explanation

Solution

= ∫1+x+x+x2x+1+x\int \frac { 1 + x + \sqrt { x + x ^ { 2 } } } { \sqrt { x } + \sqrt { 1 + x } } dx= dx

=

dx = 23\frac { 2 } { 3 } (1 + x)3/2 + C