-1-x-x2 d x is equal to

The correct option is B 2(1+x^1/3)^3/2+C∫√(1+√(x))/√(x^2)dx = ∫ x^ 2/3 ( 1+x^1/3 )^1/2 dx =∫ x^ 2/3(1+x^1/3 )^1/2dx 1+x^1/3=t^2 x^ 2/3dx=6 t dt =∫ 6 t^2dt =2t^ ...

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Byju's Answer

Standard XII

Mathematics

Binomial Integral

∫√1+√x/√x2 d ...

Question

$\int \frac{\sqrt{1 + \sqrt[3]{x}}}{\sqrt[3]{x^{2}}} d x$ is equal to

(1 + x^{1 / 3})^{3 / 2} + C

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- (1 + x^{1 / 3})^{3 / 2} + C

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2 (1 + x^{1 / 3})^{3 / 2} + C

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None of these

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Solution

The correct option is C $2 (1 + x^{1 / 3})^{3 / 2} + C$
$\int \frac{\sqrt{1 + \sqrt[3]{x}}}{\sqrt[3]{x^{2}}} d x = \int x^{- \frac{2}{3}} {(1 + x^{\frac{1}{3}})}^{1 / 2} d x$
$= \int x^{- 2 / 3} {(1 + x^{1 / 3})}^{1 / 2} d x$
$1 + x^{1 / 3} = t^{2}$
$x^{- 2 / 3} d x = 6 t d t$
$= \int 6 t^{2} d t$
$= 2 t^{3} + c$
$= 2 {(1 + x^{3})}^{3 / 2} + c$

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$\int \frac{\sqrt{1 + \sqrt[3]{x}}}{\sqrt[3]{x^{2}}} d x$ is equal to