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How to do ʃ sin²x cos³x dx?

0 votes

please help

integration

asked Apr 29, 2014 in CALCULUS by anonymous

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1 Answer

0 votes

Apply integral reduction

$I_{m,n} = \int \sin^m{ax}\cos^n{ax}dx\,\!$ $I_{m,n} = \begin{cases} -\frac{\sin^{m-1}{ax}\cos^{n+1}{ax}}{a(m+n)}+\frac{m-1}{m+n}I_{m-2,n} \\ \frac{\sin^{m+1}{ax}\cos^{n-1}{ax}}{a(m+n)}+\frac{n-1}{m+n}I_{m,n-2} \\ \end{cases}\,\!$

m = 2 , n = 3, a = 1.

Now the value of

By substitution method

Apply derivative on each side with respect of x .

Form equation (1)

answered Apr 29, 2014 by david Expert

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