What is the integral of (2x^2+2x-3)^{35}(2x+1) ?

The integral of (2x^2+2x-3)^{35}(2x+1) is 1/72 (2x^2+2x-3)^{36}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^2+2x-3)^{35}(2x+1)

\int (2 x^{2} + 2 x - 3)^{35} (2 x + 1) d x

\frac{1}{72} (2 x^{2} + 2 x - 3)^{36} + C

Solution steps

\int (2 x^{2} + 2 x - 3)^{35} (2 x + 1) d x

Apply u-substitution

: \int \frac{u ^{35}}{2} d u

= \int \frac{u ^{35}}{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^{35} d u

Apply the Power Rule

: \frac{u ^{36}}{36}

= \frac{1}{2} \cdot \frac{u ^{36}}{36}

Substitute back

u = 2 x^{2} + 2 x - 3

= \frac{1}{2} \cdot \frac{( 2 x ^{2} + 2 x - 3 ) ^{36}}{36}

Simplify

\frac{1}{2} \cdot \frac{( 2 x ^{2} + 2 x - 3 ) ^{36}}{36} : \frac{1}{72} (2 x^{2} + 2 x - 3)^{36}

= \frac{1}{72} (2 x^{2} + 2 x - 3)^{36}

Add a constant to the solution

= \frac{1}{72} (2 x^{2} + 2 x - 3)^{36} + C

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

\int \frac{3 e ^{x}}{e ^{2 x} + 9 e ^{x} + 20} d x

\int 6 y e^{5 y^{2}} d y

\int z sin (z) cos (z) d z

\int 1 - cos (\frac{x}{2}) d x

What is the integral of (2x^2+2x-3)^{35}(2x+1) ?
The integral of (2x^2+2x-3)^{35}(2x+1) is 1/72 (2x^2+2x-3)^{36}+C