Question

FIND..................

Answer 1

To Integrate sin^3x cos^2x dx

=∫sinx (sin^2x)cos^2x dx

=∫sinx (1−cos^2x) cos^2xdx

=∫(sinx cos^2x−sinx cos^4x)dx

=−∫cos^2x(−sinx) dx+∫cos^4x(−sinx)dx

=−cos3x/3+cos5x/5+C

=1/15cos^3x(3cos^2x−5)+C

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Answer 2

To Integrate sin^3x cos^2x dx

=∫sinx (sin^2x)cos^2x dx

=∫sinx (1−cos^2x) cos^2xdx

=∫(sinx cos^2x−sinx cos^4x)dx

=−∫cos^2x(−sinx) dx+∫cos^4x(−sinx)dx

=−cos3x/3+cos5x/5+C

=1/15cos^3x(3cos^2x−5)+C