What is the integral of e^{20x} ?

The integral of e^{20x} is 1/20 e^{20x}+C

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integral of e^{20x}

\int e^{20 x} d x

\frac{1}{20} e^{20 x} + C

Solution steps

\int e^{20 x} d x

Apply u-substitution

= \int e^{u} \frac{1}{20} d u

Take the constant out:

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

= \frac{1}{20} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{20} e^{u}

Substitute back

u = 20 x

= \frac{1}{20} e^{20 x}

Add a constant to the solution

= \frac{1}{20} e^{20 x} + C

t an g e n t f (x) = 2 x^{4}, at x = - 2

\int cos (x) ln (x) d x

\frac{\partial}{\partial x} (x cos (y) + y)

\frac{d}{d x} (e^{\frac{x}{8}} cos (\frac{x}{8}))

x \to 0 lim (sin (x) + 1)