What is the integral of 4e^{4x+5} ?

The integral of 4e^{4x+5} is e^{4x+5}+C

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integral of 4e^{4x+5}

\int 4 e^{4 x + 5} d x

e^{4 x + 5} + C

Solution steps

\int 4 e^{4 x + 5} d x

Take the constant out:

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

= 4 \cdot \int e^{4 x + 5} d x

Apply u-substitution

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

= 4 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = 4 x + 5

= 4 \cdot \frac{1}{4} e^{4 x + 5}

Simplify

4 \cdot \frac{1}{4} e^{4 x + 5} : e^{4 x + 5}

= e^{4 x + 5}

Add a constant to the solution

= e^{4 x + 5} + C

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