What is the integral of e^{2x} ?

The integral of e^{2x} is 1/2 e^{2x}+C

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integral of e^{2x}

integral

e^{2 x}

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

Solution steps

\int e^{2 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{2} d u

= \int e^{u} \frac{1}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

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

Substitute back

u = 2 x

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

Add a constant to the solution

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

f (x) = - \frac{7}{x}, at x = - 3

f (x) = (2 sin^{3} (x) - 5 x)^{\frac{5}{3}}

(3, - 5), (7, 9)

2 x \cdot e^{x^{2}}

f (x, y) = - e^{x - y^{2} + x y}