en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1+e^x

Solution

\int 1 + e^{x} d x

Solution

x + e^{x} + C

Solution steps

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

\int 1 d x = x

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

= x + e^{x}

Add a constant to the solution

= x + e^{x} + C

Popular Examples

derivative of ln(sqrt(x^8+19))

\frac{d}{d x} (ln (x^{8} + 19))

derivative of 2cos(x^3-2/x)

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

\frac{d}{d t} (t^{3})

tangent of f(x)=x^2+3x+1,(-1,-1)tangent of

f (x) = x^{2} + 3 x + 1, (- 1, - 1)

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

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

Frequently Asked Questions (FAQ)

What is the integral of 1+e^x ?
The integral of 1+e^x is x+e^x+C