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0-pi-4-1-sinx-cosx-sin-6-x-dx-equals-




Question Number 108303 by Sayantan chakraborty last updated on 16/Aug/20
∫_0 ^(π/4) (1/((sinx+cosx)))sin^6 x dx equals
$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{1}}{\left({sinx}+{cosx}\right)}{sin}^{\mathrm{6}} {x}\:{dx}\:{equals} \\ $$
Answered by Sayantan chakraborty last updated on 16/Aug/20
Answer:(1/4)((1/( (√2)))ln((√)2+1)+1).
$$\mathrm{Answer}:\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{ln}\left(\sqrt{}\mathrm{2}+\mathrm{1}\right)+\mathrm{1}\right). \\ $$

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