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Popular >

integral of (e^t)^2

Solution

\int (e^{t})^{2} d t

Solution

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

Solution steps

\int (e^{t})^{2} d t

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = e^{t}

= \frac{( e ^{t} ) ^{2}}{2}

Simplify

\frac{( e ^{t} ) ^{2}}{2} : \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

integral of x^3sec^2(y)

\int x^{3} sec^{2} (y) d y

y^{''}+(y^')/x =2x+1

y^{^{''}} + \frac{y ^{^{'}}}{x} = 2 x + 1

taylor arctan(x)taylor

arctan (x)

y^{''}-7y^'+3y=xe^x

y^{^{''}} - 7 y^{^{'}} + 3 y = x e^{x}

limit as x approaches 0 of (5x^2-4x)/x

x \to 0 lim (\frac{5 x ^{2} - 4 x}{x})

Frequently Asked Questions (FAQ)

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