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Question Number 82617 by necxxx last updated on 23/Feb/20

$$\int \sin \left(101x\right){\left(sinx\right)}^{99}dx$$

Answered by TANMAY PANACEA last updated on 23/Feb/20

$$\int sin(n+1){xsin}^{n-1}xdxn=100$$$$\int (sinnxcosx+cosnxsinx){sin}^{n-1}xdx$$$$\int ({sinnxcosxsin}^{n-1}x+{cosnxsin}^{n}x)dx$$$$\int (sinnx\times \frac{d\left({sin}^{n}x\right)}{dx}\times \frac{1}{n}+{sin}^{n}x\times \frac{d\left(sinnx\right)}{dx}\times \frac{1}{n})dx$$$$\frac{1}{n}\int \frac{d}{dx}(sinnx.{sin}^{n}x)dx$$$$\frac{1}{n}(sinnx.{sin}^{n}x)+c$$$$\frac{1}{100}\left(sin100{xsin}^{100}x\right)+c$$$$$$

Commented by peter frank last updated on 23/Feb/20

$$helpqn74411$$

Commented by TANMAY PANACEA last updated on 23/Feb/20

$$okletmesee$$

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