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

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

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

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

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

Solution steps

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

\int \frac{1}{5 - 4 x ^{2}} d x

\int_{0}^{2} 2 x - x^{3} d x

\int \frac{x + 5}{16 - ( x - 4 ) ^{2}} d x

f (x) = \frac{1}{5 x}

x \to 0 + lim (2 x + 8)

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