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Graxum

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- Homework Statement
- evaluate the integral ##\int 75 \sin^3(x) \cos^2 (x)dx##

- Relevant Equations
- u-substitution

my notebook says that we can rewrite the integral

$$\int {75\sin^3(x) \cos^2(x)dx}$$

as

$$\int {75 \cos^2(x)\sin(x)dx} - \int {75\sin(x)\cos^4(x)dx}$$

however, i have literally no idea how it got to this point, and i unfortunately can't really provide an "attempt at a solution" for this. If we can seperate integrals with multiplication in their integrands in such a way, why don't we use this more often?

$$\int {75\sin^3(x) \cos^2(x)dx}$$

as

$$\int {75 \cos^2(x)\sin(x)dx} - \int {75\sin(x)\cos^4(x)dx}$$

however, i have literally no idea how it got to this point, and i unfortunately can't really provide an "attempt at a solution" for this. If we can seperate integrals with multiplication in their integrands in such a way, why don't we use this more often?

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