What is the integral of 6e^{5x} ?

The integral of 6e^{5x} is 6/5 e^{5x}+C

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integral of 6e^{5x}

\int 6 e^{5 x} d x

\frac{6}{5} e^{5 x} + C

Solution steps

\int 6 e^{5 x} d x

Take the constant out:

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

= 6 \cdot \int e^{5 x} d x

Apply u-substitution

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

= 6 \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

= 6 \cdot \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= 6 \cdot \frac{1}{5} e^{u}

Substitute back

u = 5 x

= 6 \cdot \frac{1}{5} e^{5 x}

Simplify

6 \cdot \frac{1}{5} e^{5 x} : \frac{6}{5} e^{5 x}

= \frac{6}{5} e^{5 x}

Add a constant to the solution

= \frac{6}{5} e^{5 x} + C

(7, - 6), (4, - 6)

f (x) = e^{2 x + 1}

\int v^{- \frac{2}{3}} d v

\frac{1}{( 2 x )}