Write a value of ^3x dx - Vidyadip

Question

Write a value of $\int\sin^3\text{x}\cos\text{x dx}$

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Answer

Let $\text{I}=\int\sin^3\text{x}\cos\text{x dx}$
Let $\sin\text{x}=\text{t}$
$\cos\text{x dx}=\text{dt}$
$\therefore\ \text{I}=\int\text{t}^3\text{ dt}$
$=\frac{\text{t}^4}{4}+\text{C}$
$=\frac{\sin^4\text{x}}{4}+\text{C}$ $(\because\text{t}=\sin\text{x})$

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