en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 12x^2+e^x

Solution

\int 12 x^{2} + e^{x} d x

Solution

4 x^{3} + e^{x} + C

Solution steps

\int 12 x^{2} + e^{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 12 x^{2} d x + \int e^{x} d x

\int 12 x^{2} d x = 4 x^{3}

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

= 4 x^{3} + e^{x}

Add a constant to the solution

= 4 x^{3} + e^{x} + C

Popular Examples

derivative of ln(arctan(4x^3))

\frac{d}{d x} (ln (arctan (4 x^{3})))

integral of 2^{x+2}

\int 2^{x + 2} d x

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

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

laplacetransform 10sin(3t)laplace transform

10 sin (3 t)

integral of (x+pi)sin(nx)

\int (x + π) sin (n x) d x

Frequently Asked Questions (FAQ)

What is the integral of 12x^2+e^x ?
The integral of 12x^2+e^x is 4x^3+e^x+C