What is the integral of cos^3(x)sin^8(x) ?

The integral of cos^3(x)sin^8(x) is (sin^9(x))/9-(sin^{11}(x))/(11)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos^3(x)sin^8(x)

\int cos^{3} (x) sin^{8} (x) d x

\frac{sin ^{9} ( x )}{9} - \frac{sin ^{11} ( x )}{11} + C

Solution steps

\int cos^{3} (x) sin^{8} (x) d x

Rewrite using trig identities

= \int (1 - sin^{2} (x)) cos (x) sin^{8} (x) d x

Apply u-substitution

: \int u^{8} (1 - u^{2}) d u

= \int u^{8} (1 - u^{2}) d u

Expand

u^{8} (1 - u^{2}) : u^{8} - u^{10}

= \int u^{8} - u^{10} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{8} d u - \int u^{10} d u

\int u^{8} d u = \frac{u ^{9}}{9}

\int u^{10} d u = \frac{u ^{11}}{11}

= \frac{u ^{9}}{9} - \frac{u ^{11}}{11}

Substitute back

u = sin (x)

= \frac{sin ^{9} ( x )}{9} - \frac{sin ^{11} ( x )}{11}

Add a constant to the solution

= \frac{sin ^{9} ( x )}{9} - \frac{sin ^{11} ( x )}{11} + C

\int \frac{2 x ^{2} - 10 x + 14}{( x - 3 ) ^{3}} d x

\int x x^{4} + 81 d x

\int \frac{x ^{3} - 2 x ^{2} + 5 x}{x ^{2}} d x

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

\int tan (x) ln (x) cos (x) d x

What is the integral of cos^3(x)sin^8(x) ?
The integral of cos^3(x)sin^8(x) is (sin^9(x))/9-(sin^{11}(x))/(11)+C