What is the integral of 9e^{9x} ?

The integral of 9e^{9x} is e^{9x}+C

Popular >

integral of 9e^{9x}

\int 9 e^{9 x} d x

e^{9 x} + C

Solution steps

\int 9 e^{9 x} d x

Take the constant out:

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

= 9 \cdot \int e^{9 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{9} d u

= 9 \cdot \int e^{u} \frac{1}{9} d u

Take the constant out:

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

= 9 \cdot \frac{1}{9} \cdot \int e^{u} d u

Use the common integral:

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

= 9 \cdot \frac{1}{9} e^{u}

Substitute back

u = 9 x

= 9 \cdot \frac{1}{9} e^{9 x}

Simplify

9 \cdot \frac{1}{9} e^{9 x} : e^{9 x}

= e^{9 x}

Add a constant to the solution

= e^{9 x} + C

\frac{\partial}{\partial x} (8 x y e^{- x^{2} - y^{2}})

\int \frac{3 x + 1}{x ^{2} - 4 x + 7} d x

\int_{7}^{10} \frac{y}{y ^{2} - 3 y - 4} d y

x \to + 2 lim (4 tan (3 x - 3))

\int_{6}^{9} \frac{1}{x ^{2} - 1} d x