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Popular >

integral of cos^1(x)sin^3(x)

Solution

\int cos^{1} (x) sin^{3} (x) d x

Solution

\frac{sin ^{4} ( x )}{4} + C

Solution steps

\int cos^{1} (x) sin^{3} (x) d x

Simplify

sin^{3} (x) : sin^{2} (x) sin (x)

= \int cos^{1} (x) sin^{2} (x) sin (x) d x

Simplify

cos^{1} (x) sin^{2} (x) sin (x) : sin^{3} (x) cos (x)

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

= \frac{sin ^{4} ( x )}{4}

Add a constant to the solution

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

Graph

Popular Examples

integral of (15)/(400+5t)

\int \frac{15}{400 + 5 t} d t

integral of (sec^2(2x))/(tan(2x))

\int \frac{sec ^{2} ( 2 x )}{tan ( 2 x )} d x

integral of b/a 1/(sqrt(x^2+a^2))

\int \frac{b}{a} \frac{1}{x ^{2} + a ^{2}} d x

integral of sin(x/x)

\int sin (\frac{x}{x}) d x

integral of (3x-7)^2

\int (3 x - 7)^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of cos^1(x)sin^3(x) ?
The integral of cos^1(x)sin^3(x) is (sin^4(x))/4+C