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

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

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integral of e^{x/6}

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

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

Solution steps

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

Apply u-substitution

: \int e^{u} \cdot 6 d u

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

Take the constant out:

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

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

Use the common integral:

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

= 6 e^{u}

Substitute back

u = \frac{x}{6}

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

Add a constant to the solution

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

\frac{2 t}{2 + t}

\int_{1}^{2} \frac{x}{x - 1} d x

\frac{7 - x e ^{x}}{x + e ^{x}}

x \to 1 lim (\frac{x - 1}{x - 1})