What is the integral of e^{5y} ?

The integral of e^{5y} is 1/5 e^{5y}+C

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integral of e^{5y}

\int e^{5 y} d y

\frac{1}{5} e^{5 y} + C

Solution steps

\int e^{5 y} d y

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

= \int e^{u} \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{5} e^{u}

Substitute back

u = 5 y

= \frac{1}{5} e^{5 y}

Add a constant to the solution

= \frac{1}{5} e^{5 y} + C

\int 12 gx d x

f (t) = arctan (t)

a^{2} + cos^{2} (x)

y = \frac{100}{25 + x ^{2}}, y = 1

(4 y + 2 x - 5) d x + (6 y + 4 x - 1) d y = 0