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Find the value of int(0)^(pi//2)cos^(5)x...

Find the value of `int_(0)^(pi//2)cos^(5)x sin ^(7)xdx`

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`I=int_(0)^(pi/2)cos^(5)x(sin(6x+x))dx`
`I=ubrace(int_(0)^((pi)/2) sin6xcos^(6)x dx)_(I_(1))+ubrace(int_(0)^((pi)/2)ubrace(cos6x)_(I)ubrace(sinxcos^(5)x)_(II)dx)_(I_(2))`
`I_(2)=-cos 6x(cosx)/6|_(0)^((pi)/2)-int_(0)^((pi)/2)6 sin 6x(cos^(6)x)/6 dx`
`:. I=1/6`
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