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

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

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integral of sin(θ)cos^3(θ)

\int sin (θ) cos^{3} (θ) d θ

- \frac{cos ^{4} ( θ )}{4} + C

Solution steps

\int sin (θ) cos^{3} (θ) d θ

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 (θ)

= - \frac{cos ^{4} ( θ )}{4}

Add a constant to the solution

= - \frac{cos ^{4} ( θ )}{4} + C

x \to 1 lim (x^{3} - 5 x)

(\frac{1}{1 - x ^{2}})^{^{'}}

y^{^{'}} = 7 y - x

x \to 5 - lim (- (x - 3)^{2})

\int \frac{1}{y ( y - 1 )} d y

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