Question

Integrate W.R. to x the following: sin³x​

Answer 1

$\frac{cos^{3} x}{3} - cosx + c$

Step-by-step explanation:

$we \: \: know \: \: \boxed{sin ^{2}x = 1 - cos^{2}x } \\ Now, \: \: \int sin^{3} xdx \\ = \int sin^{2}x.sinxdx \\ = \int (1 - cos^{2}x )sinxdx \\ let, \: y = cosx \\ Differentiating \: \: with \: \: respect \: \: to \: \: x \\ dy = - sinxdx \\ - dy = sinxdx \\ putting \: \: values \\ - \int (1 - {y}^{2} )dy \\ = \int ( {y}^{2} - 1 )dy \\ = \frac{ {y}^{3} }{3} - y + c \\ putting \: \: value \: \: of \: \: y \: \: then \\ = \frac{cos^{3} x}{3} - cosx + c$