What is the integral of (3e^x-1/3 x^3) ?

The integral of (3e^x-1/3 x^3) is 3e^x-(x^4)/(12)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3e^x-1/3 x^3)

\int (3 e^{x} - \frac{1}{3} x^{3}) d x

3 e^{x} - \frac{x ^{4}}{12} + C

Solution steps

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

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

\int \frac{1}{3} x^{3} d x = \frac{x ^{4}}{12}

= 3 e^{x} - \frac{x ^{4}}{12}

Add a constant to the solution

= 3 e^{x} - \frac{x ^{4}}{12} + C

\int 13 x e^{- x^{2}} d x

\int \frac{- 4 x}{e ^{x^{2}}} d x

t an g e n t f (x) = x - \frac{1}{x} + ln (x), at x = 1

t an g e n t y = 16 x sin (x), (\frac{π}{2}, 8 π)

\frac{\partial}{\partial y} (x ln (y + z))

What is the integral of (3e^x-1/3 x^3) ?
The integral of (3e^x-1/3 x^3) is 3e^x-(x^4)/(12)+C