What is the integral of e^{y/3} ?

The integral of e^{y/3} is 3e^{y/3}+C

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integral of e^{y/3}

\int e^{\frac{y}{3}} d y

3 e^{\frac{y}{3}} + C

Solution steps

\int e^{\frac{y}{3}} d y

Apply u-substitution

: \int e^{u} \cdot 3 d u

= \int e^{u} \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int e^{u} d u

Use the common integral:

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

= 3 e^{u}

Substitute back

u = \frac{y}{3}

= 3 e^{\frac{y}{3}}

Add a constant to the solution

= 3 e^{\frac{y}{3}} + C

\frac{x ^{2} - 4 x + 2}{x + 3}

x \to 1 lim (x^{2} - 1)

\int 3 x^{2} - 5 d x

\frac{e ^{1 - s}}{s ^{2} - 1}

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