What is the integral of cos^3(x)*sin(x) ?

The integral of cos^3(x)*sin(x) is -(cos^4(x))/4+C

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integral of cos^3(x)*sin(x)

\int cos^{3} (x) \cdot sin (x) d x

- \frac{cos ^{4} ( x )}{4} + C

Solution steps

\int cos^{3} (x) sin (x) d x

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = cos (x)

= - \frac{cos ^{4} ( x )}{4}

Add a constant to the solution

= - \frac{cos ^{4} ( x )}{4} + C

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{2 x}

\int_{2}^{3} 3 x d x

\int_{0}^{\frac{π}{4}} (tan (x))^{2} d x

\frac{d}{d x} (- 6 x^{3})

x \to - 1 lim (3 f (x) - 2 h (x))

What is the integral of cos^3(x)*sin(x) ?
The integral of cos^3(x)*sin(x) is -(cos^4(x))/4+C