What is the integral of e^{6x} ?

The integral of e^{6x} is 1/6 e^{6x}+C

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integral of e^{6x}

\int e^{6 x} d x

\frac{1}{6} e^{6 x} + C

Solution steps

\int e^{6 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{6} d u

= \int e^{u} \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{6} e^{u}

Substitute back

u = 6 x

= \frac{1}{6} e^{6 x}

Add a constant to the solution

= \frac{1}{6} e^{6 x} + C

\int sin^{2} (ln (x)) d x

\int \frac{2 x - 9}{x ^{2} - 9 x + 1} d x

\frac{\partial}{\partial x} (\frac{x y}{( x ^{2} - y ^{2} ) ^{2}})

y = x^{2} + 1, (- 2, 5)

x, at 25