en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^6(x+4)

Solution

\int x^{6} (x + 4) d x

Solution

\frac{x ^{8}}{8} + \frac{4 x ^{7}}{7} + C

Solution steps

\int x^{6} (x + 4) d x

Expand

x^{6} (x + 4) : x^{7} + 4 x^{6}

= \int x^{7} + 4 x^{6} 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 x^{7} d x + \int 4 x^{6} d x

\int x^{7} d x = \frac{x ^{8}}{8}

\int 4 x^{6} d x = \frac{4 x ^{7}}{7}

= \frac{x ^{8}}{8} + \frac{4 x ^{7}}{7}

Add a constant to the solution

= \frac{x ^{8}}{8} + \frac{4 x ^{7}}{7} + C

Popular Examples

sum from n=1 to infinity of n/(n+2)

n = 1 \sum \infty \frac{n}{n + 2}

y^{''}+12y^'+85y=0

y^{^{''}} + 12 y^{^{'}} + 85 y = 0

integral of 2e^{-5x}

\int 2 e^{- 5 x} d x

derivative of-2x^{2/3}-4 derivative of

- 2 x^{\frac{2}{3}} - 4

integral of (5x^2)/(x+7)

\int \frac{5 x ^{2}}{x + 7} d x

Frequently Asked Questions (FAQ)

What is the integral of x^6(x+4) ?
The integral of x^6(x+4) is (x^8)/8+(4x^7)/7+C