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Question: \(\int \frac { d x } { \sqrt { x + 1 } + ( x + 1 ) ^ { \frac { 1 } { 3 } } }\) is equal to...

∫dxx+1+(x+1)13\int \frac { d x } { \sqrt { x + 1 } + ( x + 1 ) ^ { \frac { 1 } { 3 } } } is equal to

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None of these

Answer
Explanation

Solution

Here I = ∫6p5dpp3+p2\int \frac { 6 p ^ { 5 } d p } { p ^ { 3 } + p ^ { 2 } }((x + 1) = p6, then dx = 6p5 dp).

=

= 6p33−6p22+6p−6ln⁡(p+1)\frac { 6 p ^ { 3 } } { 3 } - \frac { 6 p ^ { 2 } } { 2 } + 6 p - 6 \ln ( p + 1 )+ c

2p3−3p2+6p−6ln⁡(1+p)+c2 p ^ { 3 } - 3 p ^ { 2 } + 6 p - 6 \ln ( 1 + p ) + c, where p=(x+1)16p = ( x + 1 ) ^ { \frac { 1 } { 6 } }