What is the integral of 100e^{4x} ?

The integral of 100e^{4x} is 25e^{4x}+C

integral of 100e^{4x}

\int 100 e^{4 x} d x

25 e^{4 x} + C

Solution steps

\int 100 e^{4 x} d x

Take the constant out:

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

= 100 \cdot \int e^{4 x} d x

Apply u-substitution

= 100 \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

= 100 \cdot \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= 100 \cdot \frac{1}{4} e^{u}

Substitute back

u = 4 x

= 100 \cdot \frac{1}{4} e^{4 x}

Simplify

100 \cdot \frac{1}{4} e^{4 x} : 25 e^{4 x}

= 25 e^{4 x}

Add a constant to the solution

= 25 e^{4 x} + C

\int e^{x} (1 + e^{x})^{3} d x

\int \frac{( arctan ( ln ( x + 3 ) ) )}{x + 3} d x

\int 32 x^{2} d x

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

\int \frac{1}{25 + 36 x ^{2}} d x