^3(2x+1)dx - Vidyadip

Question

$\int\sin^3(2\text{x}+1)\text{dx}$

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Answer

We need to evaluate $\int\sin^3(2\text{x}+1)\text{dx}$
By using the formula
$\sin3\theta=-4\sin^3\theta+3\sin\theta$
$\therefore\sin^3(2\text{x}+1)=\frac{3\sin(2\text{x}+1)-\sin3(2\text{x}+1)}{4}$
$\int\sin^3(2\text{x}+1)\text{dx}$
$=\int\frac{3\sin(2\text{x}+1)-\sin3(2\text{x}+1)}{4}\text{dx}$
$=-\frac{3}{8}\cos(2\text{x}+1)+\frac{1}{24}\cos3(2\text{x}+1)+\text{C}$

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