What is the integral of e^{4x+7} ?

The integral of e^{4x+7} is 1/4 e^{4x+7}+C

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integral of e^{4x+7}

\int e^{4 x + 7} d x

\frac{1}{4} e^{4 x + 7} + C

Solution steps

\int e^{4 x + 7} d x

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 x + 7

= \frac{1}{4} e^{4 x + 7}

Add a constant to the solution

= \frac{1}{4} e^{4 x + 7} + C

e^{x} \cdot sin (2 x)

f (t) = t^{2} + 6 t - 3

f (x) = 2 x^{4}, (- 2, 32)

\int \frac{x + 3}{x ^{2} - 1} d x

\frac{d}{d x} (18 x e^{x^{2}})