What is the integral of 2x^3+5x^2-2x+1 ?

The integral of 2x^3+5x^2-2x+1 is (x^4)/2+(5x^3)/3-x^2+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x^3+5x^2-2x+1

\int 2 x^{3} + 5 x^{2} - 2 x + 1 d x

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

Solution steps

\int 2 x^{3} + 5 x^{2} - 2 x + 1 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 2 x^{3} d x + \int 5 x^{2} d x - \int 2 x d x + \int 1 d x

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 1 d x = x

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

Add a constant to the solution

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

f (x) = \frac{4}{x}, at x = \frac{1}{9}

\int 16 x ln (5 x) d x

\frac{\partial}{\partial x} (x (x^{2} + y^{2})^{- 1})

f (x) = 4 x cos (x)

x - 9

What is the integral of 2x^3+5x^2-2x+1 ?
The integral of 2x^3+5x^2-2x+1 is (x^4)/2+(5x^3)/3-x^2+x+C