What is the integral of cos^{19}(x)sin(x) ?

The integral of cos^{19}(x)sin(x) is -(cos^{20}(x))/(20)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos^{19}(x)sin(x)

\int cos^{19} (x) sin (x) d x

- \frac{cos ^{20} ( x )}{20} + C

Solution steps

\int cos^{19} (x) sin (x) d x

Apply u-substitution

: \int - u^{19} d u

= \int - u^{19} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{19} d u

Apply the Power Rule

: \frac{u ^{20}}{20}

= - \frac{u ^{20}}{20}

Substitute back

u = cos (x)

= - \frac{cos ^{20} ( x )}{20}

Add a constant to the solution

= - \frac{cos ^{20} ( x )}{20} + C

\int (4 x^{\frac{2}{3}} - 4 x^{\frac{1}{5}}) d x

\int - \frac{x ^{3} + 2}{6} d x

\int (2 + x + y e^{y}) d y

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

\int \frac{1}{( 5 x + 2 ) ^{4}} d x

What is the integral of cos^{19}(x)sin(x) ?
The integral of cos^{19}(x)sin(x) is -(cos^{20}(x))/(20)+C