en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^2-3)^2

Solution

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

Solution

\frac{4 x ^{5}}{5} - 4 x^{3} + 9 x + C

Solution steps

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

Expand

(2 x^{2} - 3)^{2} : 4 x^{4} - 12 x^{2} + 9

= \int 4 x^{4} - 12 x^{2} + 9 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 4 x^{4} d x - \int 12 x^{2} d x + \int 9 d x

\int 4 x^{4} d x = \frac{4 x ^{5}}{5}

\int 12 x^{2} d x = 4 x^{3}

\int 9 d x = 9 x

= \frac{4 x ^{5}}{5} - 4 x^{3} + 9 x

Add a constant to the solution

= \frac{4 x ^{5}}{5} - 4 x^{3} + 9 x + C

Popular Examples

limit as x approaches 2 of sqrt(x/(x-2))

x \to 2 lim (\frac{x}{x - 2})

derivative of cos(x)+isin(x)derivative of

cos (x) + i sin (x)

integral of e^{2x}x

\int e^{2 x} x d x

integral of 9x^2-24x-36

\int 9 x^{2} - 24 x - 36 d x

derivative of cos(1-4x)

\frac{d}{d x} (cos (1 - 4 x))

Frequently Asked Questions (FAQ)

What is the integral of (2x^2-3)^2 ?
The integral of (2x^2-3)^2 is (4x^5)/5-4x^3+9x+C