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  • The value of <img alt="\int \frac{\sin ^{8}x-\cos ^{8}x}{1-2\sin ^{2}x\cos ^{2}x}\: dx" src="https://learn.careers360.com/latex-image/?%5Cint%20%5Cfrac%7B%5Csin%20%5E%7

The value of \int \frac{\sin ^{8}x-\cos ^{8}x}{1-2\sin ^{2}x\cos ^{2}x}\: dxis :

 

Option: 1

\frac{1}{2}\sin \, 2x+C
 


Option: 2

-\frac{1}{2}\sin \, 2x+C


Option: 3

-\frac{1}{2}\sin \, x+C

 


Option: 4

-\sin^{2} \, x+C


Answers (1)

best_answer

 

Integration of trigonometric function of power m -

\int sin^{m}xdx    and 

 \int cos^{m}xdx

- wherein

for m=2,

sin^{2}x=\frac{1-cos 2x}{2}

for m=3,

sin3x=3sinx-4sin^{3}x

 

 

\int \frac{\sin^{8}x-\cos^{8}x}{\sin^{4}x+\cos^{4}x}dx=\int \left ( \sin^{4}x-\cos^{4}x \right )dx

=\int \left ( \sin^{2} x-\cos^{2}x\right )dx=-\frac{1}{2}\sin2x+C

Posted by

manish painkra

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