What is the integral of e^{4y} ?

The integral of e^{4y} is 1/4 e^{4y}+C

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integral of e^{4y}

\int e^{4 y} d y

\frac{1}{4} e^{4 y} + C

Solution steps

\int e^{4 y} d y

Apply u-substitution

: \int e^{u} \frac{1}{4} d u

= \int e^{u} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = 4 y

= \frac{1}{4} e^{4 y}

Add a constant to the solution

= \frac{1}{4} e^{4 y} + C

x \to 0 + lim (x^{6 x})

s

\int 400 - x^{2} d x

5 cos (3 x), 5 sin (6 x), [0, \frac{π}{6}]