en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4x^3-x

Solution

\int 4 x^{3} - x d x

Solution

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

Solution steps

\int 4 x^{3} - x 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^{3} d x - \int x d x

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

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

= x^{4} - \frac{x ^{2}}{2}

Add a constant to the solution

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

Popular Examples

integral of (8x^2+x)/((16x^3+3x^2)^2)

\int \frac{8 x ^{2} + x}{( 16 x ^{3} + 3 x ^{2} ) ^{2}} d x

integral of (4x^2-3)^2

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

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

\int \frac{2 x ^{4} - 2 x ^{3} + x + 1}{x ^{3} - x ^{2}} d x

integral of 1/((1-x^2)x^2)

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

integral of (2/(e^{-x)}-1/(2x))

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

Frequently Asked Questions (FAQ)

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