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

x \to \infty lim (\frac{( 2 x - 1 ) ( 3 - x )}{( x - 1 ) ( x + 3 )})

y^{^{'}} = \frac{2 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

\int - \frac{sin ( 2 x )}{4} d x

y^{^{''}} + y^{^{'}} + y = cos (t)

\int \frac{7 x ^{6} + 2}{x ^{7} + 2 x} d x

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