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We can derive reduction formulas for the integral of the form \( \int \sin ^{n} x d x, \int \cos ^{n} x d x \int \tan ^{n} x d x \), \( \int \cot ^{n} x d x \) and other integrals of these form using integration by parts. In turn these reduction formulas can be used to compute integrals of higher power of \( \sin x, \cos x \) etc.
If \( \int \sin ^{5} x d x=-\frac{1}{5} \sin ^{4} x \cos x+A \sin ^{2} x \cos x \)
\( -\frac{8}{15} \cos x+C \) then \( A \) is equal to
(a) \( -2 / 15 \)
(b) \( -3 / 5 \)
(c) \( -4 / 15 \)
(d) \( -1 / 15 \)
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