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Popular >

integral of e^x+e^xx

Solution

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

Solution

e^{x} x + C

Solution steps

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

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

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

= e^{x} + e^{x} x - e^{x}

Simplify

= e^{x} x

Add a constant to the solution

= e^{x} x + C

Popular Examples

derivative of g(x)= 1/(sqrt(x))derivative of

g (x) = \frac{1}{x}

inverse oflaplace 6/s+(16)/(s^2+16)inverse laplace

\frac{6}{s} + \frac{16}{s ^{2} + 16}

(d^2y)/(dx^2)=0

\frac{d ^{2} y}{d x ^{2}} = 0

integral from-1 to 1 of e^x-1

\int_{- 1}^{1} e^{x} - 1 d x

limit as x approaches-1+of x^2-3

x \to - 1 + lim (x^{2} - 3)

Frequently Asked Questions (FAQ)

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