What is the integral of (x+2)(x^2+4x+2)^{10} ?

The integral of (x+2)(x^2+4x+2)^{10} is 1/22 (x^2+4x+2)^{11}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+2)(x^2+4x+2)^{10}

\int (x + 2) (x^{2} + 4 x + 2)^{10} d x

\frac{1}{22} (x^{2} + 4 x + 2)^{11} + C

Solution steps

\int (x + 2) (x^{2} + 4 x + 2)^{10} d x

Apply u-substitution

: \int \frac{u ^{10}}{2} d u

= \int \frac{u ^{10}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{10} d u

Apply the Power Rule

: \frac{u ^{11}}{11}

= \frac{1}{2} \cdot \frac{u ^{11}}{11}

Substitute back

u = x^{2} + 4 x + 2

= \frac{1}{2} \cdot \frac{( x ^{2} + 4 x + 2 ) ^{11}}{11}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} + 4 x + 2 ) ^{11}}{11} : \frac{1}{22} (x^{2} + 4 x + 2)^{11}

= \frac{1}{22} (x^{2} + 4 x + 2)^{11}

Add a constant to the solution

= \frac{1}{22} (x^{2} + 4 x + 2)^{11} + C

\int - 64 d x

n = 1 \sum \infty (- 0.2)^{n - 1}

\frac{d}{d x} (x^{2} 2 x - 7)

\int \frac{e ^{8 x}}{e ^{8 x} + 7} d x

\int \frac{1}{cos ^{3} ( x )} d x

What is the integral of (x+2)(x^2+4x+2)^{10} ?
The integral of (x+2)(x^2+4x+2)^{10} is 1/22 (x^2+4x+2)^{11}+C