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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^3-x^2+1)

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

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\int \frac{e ^{3 x}}{e ^{x} + 1} d x

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

\int \frac{ln ( tan ( x ) )}{sin ( 2 x )} d x

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

\int 4 t^{5} 2 t^{2} + 3 d t

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