sin-7-x-dx-

Question Number 142917 by ERA last updated on 07/Jun/21

$$\int\left(\boldsymbol{\mathrm{sin}}^{\mathrm{7}} \left(\boldsymbol{\mathrm{x}}\right)\right)\boldsymbol{\mathrm{dx}} \\ $$

Answered by Ar Brandon last updated on 07/Jun/21

2isin(nx)=z^n −(1/z^n ), 2isinx=z−(1/z) −128isin^7 x=z^7 −(1/z^7 )+7(z^5 −(1/z^5 ))+21(z^3 −(1/z^3 ))+35(z−(1/z)) −128sin^7 x=2sin7x+14sin5x+42sin3x+70sinx ∫sin^7 xdx=(1/(128))(((2cos7x)/7)+((14cos5x)/5)+((42cos3x)/3)+70cosx)+C

$$\mathrm{2isin}\left(\mathrm{nx}\right)=\mathrm{z}^{\mathrm{n}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{n}} },\:\mathrm{2isinx}=\mathrm{z}−\frac{\mathrm{1}}{\mathrm{z}} \\ $$$$−\mathrm{128isin}^{\mathrm{7}} \mathrm{x}=\mathrm{z}^{\mathrm{7}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{7}} }+\mathrm{7}\left(\mathrm{z}^{\mathrm{5}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{5}} }\right)+\mathrm{21}\left(\mathrm{z}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{3}} }\right)+\mathrm{35}\left(\mathrm{z}−\frac{\mathrm{1}}{\mathrm{z}}\right) \\ $$$$−\mathrm{128sin}^{\mathrm{7}} \mathrm{x}=\mathrm{2sin7x}+\mathrm{14sin5x}+\mathrm{42sin3x}+\mathrm{70sinx} \\ $$$$\int\mathrm{sin}^{\mathrm{7}} \mathrm{xdx}=\frac{\mathrm{1}}{\mathrm{128}}\left(\frac{\mathrm{2cos7x}}{\mathrm{7}}+\frac{\mathrm{14cos5x}}{\mathrm{5}}+\frac{\mathrm{42cos3x}}{\mathrm{3}}+\mathrm{70cosx}\right)+\mathrm{C} \\ $$

Facebook Tweet Pin

sin-7-x-dx-

Leave a Reply Cancel reply