What is the integral of e^{5x+1} ?

The integral of e^{5x+1} is 1/5 e^{5x+1}+C

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integral of e^{5x+1}

\int e^{5 x + 1} d x

\frac{1}{5} e^{5 x + 1} + C

Solution steps

\int e^{5 x + 1} d x

Apply u-substitution

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

= \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

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

Use the common integral:

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

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

Substitute back

u = 5 x + 1

= \frac{1}{5} e^{5 x + 1}

Add a constant to the solution

= \frac{1}{5} e^{5 x + 1} + C

y = x, y = x^{2} - 2

\int x^{2} e^{3 x^{3}} d x

\int \frac{5}{7} d x

\int \frac{x}{2 x - 1} d x

x \to 3 lim (\frac{5 x - 1}{2 x + 1})