What is the integral of cos(x)(sin(x)+1)^3 ?

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

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

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

\frac{( sin ( x ) + 1 ) ^{4}}{4} + C

Solution steps

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

= \frac{( sin ( x ) + 1 ) ^{4}}{4}

Add a constant to the solution

= \frac{( sin ( x ) + 1 ) ^{4}}{4} + C

\int \frac{2}{3 x ^{3}} d x

\int \frac{2 x + 5}{x ^{2} + 2 x + 10} d x

\int \frac{1}{3 x ^{2} - 4} d x

\int \frac{x - 1}{x} d x

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

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