What is the integral of (5x^3-2x^2+3) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5x^3-2x^2+3)

\int (5 x^{3} - 2 x^{2} + 3) d x

\frac{5 x ^{4}}{4} - \frac{2 x ^{3}}{3} + 3 x + C

Solution steps

\int 5 x^{3} - 2 x^{2} + 3 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 5 x^{3} d x - \int 2 x^{2} d x + \int 3 d x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int 3 d x = 3 x

= \frac{5 x ^{4}}{4} - \frac{2 x ^{3}}{3} + 3 x

Add a constant to the solution

= \frac{5 x ^{4}}{4} - \frac{2 x ^{3}}{3} + 3 x + C

x \to 0 lim (\frac{e ^{x} - 1}{6 x})

\int x^{4} - 4 x^{2} + 4 d x

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

\int \frac{12 x + 24}{x ^{2} + 4 x + 3} d x

3 x + 2

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