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Question Number 159597 by mathlove last updated on 19/Nov/21

Answered by mr W last updated on 19/Nov/21

$${\left(\frac{{\sin }^{2014}x\sin \left(2014x\right)}{2014}\right)}^{\prime }$$$$=\frac{2014{\sin }^{2013}x\cos x\sin \left(2014x\right)+\sin {}^{2014}x\times 2014\cos \left(2014x\right)}{2014}$$$$={\sin }^{2013}x(\cos x\sin \left(2014x\right)+\sin x\cos \left(2014x\right))$$$$={\sin }^{2013}x\sin (2014x+x)$$$$={\sin }^{2013}x\sin \left(2015x\right)$$$$\Rightarrow \int {\sin }^{2013}x\sin \left(2015x\right)dx=\frac{{\sin }^{2014}x\sin \left(2014x\right)}{2014}+C$$

Commented by mathlove last updated on 20/Nov/21

$$thenksmaster$$

Commented by infinityaction last updated on 25/Apr/22

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