en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x+e^{4x}

Solution

\int x + e^{4 x} d x

Solution

\frac{x ^{2}}{2} + \frac{1}{4} e^{4 x} + C

Solution steps

\int x + e^{4 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 x d x + \int e^{4 x} d x

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

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

= \frac{x ^{2}}{2} + \frac{1}{4} e^{4 x}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{1}{4} e^{4 x} + C

Popular Examples

(\partial)/(\partial x)(3ax^2+e^xx+e^x)

\frac{\partial}{\partial x} (3 a x^{2} + e^{x} x + e^{x})

integral from-1 to 4 of (7y)/(y^2-3y-10)

\int_{- 1}^{4} \frac{7 y}{y ^{2} - 3 y - 10} d y

limit as x approaches pi/2+of sin(x)

x \to \frac{π}{2} + lim (sin (x))

derivative of (3x^2-9^{-14})

\frac{d}{d x} ((3 x^{2} - 9)^{- 14})

tangent of y=x^2-7x+7,(0,7)tangent of

y = x^{2} - 7 x + 7, (0, 7)

Frequently Asked Questions (FAQ)

What is the integral of x+e^{4x} ?
The integral of x+e^{4x} is (x^2)/2+1/4 e^{4x}+C