Find the integral: (1-x) x d x - Vidyadip

Question

Find the integral: $\int(1-x) \sqrt{x} d x$

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Answer

$\int(1-x) \sqrt{x} d x$
= $\int\left(\sqrt{x}-x^{\frac{3}{2}}\right) d x$
= $\int x^{\frac{1}{2}} d x-\int x^{\frac{3}{2}} d x$
= $\frac{x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{x^{\frac{5}{2}}}{\frac{5}{2}}+C$
= $\frac{2}{3} x^{\frac{3}{2}}-\frac{2}{5} x^{\frac{5}{2}}+C$

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