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Popular >

integral of e^te^t

Solution

\int e^{t} e^{t} d t

Solution

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

Solution steps

\int e^{t} e^{t} d t

Apply exponent rule:

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

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

derivative of 7csc(x^5)

\frac{d}{d x} (7 csc (x^{5}))

limit as x approaches-4 of 4+x

x \to - 4 lim (4 + x)

y^{''}+y= 1/4 cos(3t)

y^{^{''}} + y = \frac{1}{4} cos (3 t)

integral from 1 to 4 of sqrt(16x^5)

\int_{1}^{4} 16 x^{5} d x

(dy)/(dx)=-2x(y-3)

\frac{d y}{d x} = - 2 x (y - 3)

Frequently Asked Questions (FAQ)

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