What is the integral of-7e^{5x} ?

The integral of-7e^{5x} is -7/5 e^{5x}+C

Popular >

integral of-7e^{5x}

\int - 7 e^{5 x} d x

- \frac{7}{5} e^{5 x} + C

Solution steps

\int - 7 e^{5 x} d x

Take the constant out:

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

= - 7 \cdot \int e^{5 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

= - 7 \cdot \int e^{u} \frac{1}{5} d u

Take the constant out:

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

= - 7 \cdot \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= - 7 \cdot \frac{1}{5} e^{u}

Substitute back

u = 5 x

= - 7 \cdot \frac{1}{5} e^{5 x}

Simplify

- 7 \cdot \frac{1}{5} e^{5 x} : - \frac{7}{5} e^{5 x}

= - \frac{7}{5} e^{5 x}

Add a constant to the solution

= - \frac{7}{5} e^{5 x} + C

\int_{0}^{\frac{π}{24}} cos (4 x) d x

\int 9 + 16 t^{2} d t

\int 1 - cos (8 x) d x

x \to 3 lim (\frac{1 - x}{x - 3})

\frac{\partial}{\partial y} (x^{2} + 2 y)