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Popular >

integral of e^xe^x

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

e^{x} e^{x} = (ee)^{x}

= \int (ee)^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{( ee ) ^{x}}{ln ( ee )}

Simplify

\frac{( ee ) ^{x}}{ln ( ee )} : \frac{1}{2} e^{2 x}

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

Add a constant to the solution

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

Popular Examples

integral of (3x)/(x^2-x-6)

\int \frac{3 x}{x ^{2} - x - 6} d x

integral from 0 to 1 of 3x(x^2+1)^4

\int_{0}^{1} 3 x (x^{2} + 1)^{4} d x

x^2(dy)/(dx)+3xy=ln(x)

x^{2} \frac{d y}{d x} + 3 x y = ln (x)

implicit xy=cot(xy)implicit derivative

x y = cot (x y)

integral of x/((z^2+x^2)^{3/2)}

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

Frequently Asked Questions (FAQ)

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