What is the integral of x^9(5+x^{10}) ?

The integral of x^9(5+x^{10}) is (x^{10})/2+(x^{20})/(20)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^9(5+x^{10})

\int x^{9} (5 + x^{10}) d x

\frac{x ^{10}}{2} + \frac{x ^{20}}{20} + C

Solution steps

\int x^{9} (5 + x^{10}) d x

Expand

x^{9} (5 + x^{10}) : 5 x^{9} + x^{19}

= \int 5 x^{9} + x^{19} d x

Apply the Sum Rule:

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

= \int 5 x^{9} d x + \int x^{19} d x

\int 5 x^{9} d x = \frac{x ^{10}}{2}

\int x^{19} d x = \frac{x ^{20}}{20}

= \frac{x ^{10}}{2} + \frac{x ^{20}}{20}

Add a constant to the solution

= \frac{x ^{10}}{2} + \frac{x ^{20}}{20} + C

\int cos (2 x) 16 d x

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

\int 9 x^{2} sin (x) d x

\int (x^{2} + 1)^{8} 2 x d x

\int - \frac{5}{1 + x ^{2}} d x

What is the integral of x^9(5+x^{10}) ?
The integral of x^9(5+x^{10}) is (x^{10})/2+(x^{20})/(20)+C