What is the integral of (x+sin(x))^4(1+cos(x)) ?

The integral of (x+sin(x))^4(1+cos(x)) is ((x+sin(x))^5)/5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+sin(x))^4(1+cos(x))

\int (x + sin (x))^{4} (1 + cos (x)) d x

\frac{( x + sin ( x ) ) ^{5}}{5} + C

Solution steps

\int (x + sin (x))^{4} (1 + cos (x)) d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = x + sin (x)

= \frac{( x + sin ( x ) ) ^{5}}{5}

Add a constant to the solution

= \frac{( x + sin ( x ) ) ^{5}}{5} + C

\int sin (\frac{1}{10} x) sin (\frac{1}{20} x) d x

\int 8 cos (\frac{x}{2}) d x

\int x x^{2} + 8 x + 21 d x

\int 324 - 9 x^{2} d x

\int 6 x - 5 d x

What is the integral of (x+sin(x))^4(1+cos(x)) ?
The integral of (x+sin(x))^4(1+cos(x)) is ((x+sin(x))^5)/5+C