How to Integrate sin^3x cos^2x | Integration of sin^3x cos^2x

The integration of sin^3x cos^2x is equal to (cos5x)/5 – (cos3x)/3 +C where C is a constant. Here we learn how to integrate sin^3x cos^2x.

Integration of sin^3x cos^2x

What is the Integration of sin3x cos2x?

Question: Find the integral of sin3x cos2x, that is,

Find ∫sin3x cos2x dx


We have:

∫sin3x cos2x dx = ∫sin2x sin x cos2x dx

⇒ ∫sin3x cos2x dx = ∫(1 -cos2x) cos2x sin x dx [by the formula sin2x = 1 -cos2x]

Put cosx =z, so that -sinx dx =dz.

∴ From above, we have that

∫sin3x cos2x dx = – ∫(1 – z2) z2 dz

= – ∫(z2 – z4) dz

= – ∫z2 dz + ∫z4 dz

= – z3/3 + z5/5 +C

= – cos3x/3 + cos5x/5 +C

So the integration of sin3x cos2x equals to – cos3x/3 + cos5x/5 +C, that is, the integral of sin cube x cos square x is given by the formula:

∫sin3x cos2x dx = – cos3x/3 + cos5x/5 +C

Related Integrals:

Integration of sinx cosx dx

Integration of sin2x dx

Integration of cos2x dx

Integral of sin3x dx


Q1: What is the integral of sin^3x cos^2x?

Answer: The integration of sin^3x cos^2x is given by ∫sin3x cos2x dx = – cos3x/3 + cos5x/5 +C where C denotes an integral constant.

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