What is the integral of e^xe^{3x} ?

The integral of e^xe^{3x} is 1/4 e^{4x}+C

Popular >

integral of e^xe^{3x}

\int e^{x} e^{3 x} d x

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

Solution steps

\int e^{x} e^{3 x} d x

Simplify

e^{x} e^{3 x} : e^{4 x}

= \int e^{4 x} 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

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

Add a constant to the solution

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

5 x 4 - 5 x, at x = - 2

5 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 9 x e^{- y}

\frac{d}{d x} (4 sec^{2} (4 x))

5 e^{t}

f (x) = \frac{7}{x}, at x = 3