find-x-2-1-x-3-dx-

Question Number 36426 by abdo.msup.com last updated on 01/Jun/18

f i n d \int x^{2} \sqrt{1 + x^{3}} d x

Answered by tanmay.chaudhury50@gmail.com last updated on 02/Jun/18

\int x^{2} \sqrt{1 + x^{3}} d x

t = 1 + x^{3}

d t = 3 x^{2} d x

= \frac{1}{3} \int \sqrt{t} d t

\frac{1}{3} \times \frac{t^{\frac{3}{2}}}{\frac{3}{2}}

\frac{2}{9} {(1 + x^{3})}^{\frac{3}{2}}