Find the value of x^ 1 / 3 x^ 2 / 3 d x : - Vidyadip

Question

Find the value of $\int \frac{\sin x^{1 / 3}}{x^{2 / 3}} d x$ :

✓

Answer

$\int \frac{\sin x^{1 / 3}}{x^{2 / 3}} d x$
Putting
$x^{1 / 3} =t$
$\frac{1}{3} x^{\frac{1}{3}-1} d x =d t$
So
$x^{-2 / 3} d x =3 d t$
$\frac{d x}{x^{2 / 3}} =3 d t$
$\Rightarrow 3 \int \sin t d t \Rightarrow 3(-\cos t)+C$
$\Rightarrow-3 \cos t+C \Rightarrow-3 \cos x^{\frac{1}{3}}+C$

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