What is the integral of 1/6 e^{6x} ?

The integral of 1/6 e^{6x} is 1/36 e^{6x}+C

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integral of 1/6 e^{6x}

\int \frac{1}{6} e^{6 x} d x

\frac{1}{36} e^{6 x} + C

Solution steps

\int \frac{1}{6} e^{6 x} d x

Take the constant out:

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

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

Apply u-substitution

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

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

Use the common integral:

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

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

Substitute back

u = 6 x

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

Simplify

\frac{1}{6} \cdot \frac{1}{6} e^{6 x} : \frac{1}{36} e^{6 x}

= \frac{1}{36} e^{6 x}

Add a constant to the solution

= \frac{1}{36} e^{6 x} + C

x \to 3 lim (x^{2} - 3 x - 10)

\int \frac{x ^{2} - 16 x + 9}{x ^{4} + 10 x ^{2} + 9} d x

y = \frac{3}{2} x

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

x \to 0 + lim (9 sin (x) ln (x))

What is the integral of 1/6 e^{6x} ?
The integral of 1/6 e^{6x} is 1/36 e^{6x}+C