What is the integral of 2x(x^2+5)^{30} ?

The integral of 2x(x^2+5)^{30} is 1/31 (x^2+5)^{31}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x(x^2+5)^{30}

\int 2 x (x^{2} + 5)^{30} d x

\frac{1}{31} (x^{2} + 5)^{31} + C

Solution steps

\int 2 x (x^{2} + 5)^{30} d x

Take the constant out:

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

= 2 \cdot \int x (x^{2} + 5)^{30} d x

Apply u-substitution

: \int \frac{u ^{30}}{2} d u

= 2 \cdot \int \frac{u ^{30}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{30} d u

Apply the Power Rule

: \frac{u ^{31}}{31}

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{31}}{31}

Substitute back

u = x^{2} + 5

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{31}}{31}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{31}}{31} : \frac{1}{31} (x^{2} + 5)^{31}

= \frac{1}{31} (x^{2} + 5)^{31}

Add a constant to the solution

= \frac{1}{31} (x^{2} + 5)^{31} + C

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

\int 3 x - 3 d x

\int sin (\frac{1}{8}) x sin (\frac{1}{16}) x d x

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

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

What is the integral of 2x(x^2+5)^{30} ?
The integral of 2x(x^2+5)^{30} is 1/31 (x^2+5)^{31}+C