What is the integral of e^{(2x)/5} ?

The integral of e^{(2x)/5} is 5/2 e^{(2x)/5}+C

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integral of e^{(2x)/5}

\int e^{\frac{2 x}{5}} d x

\frac{5}{2} e^{\frac{2 x}{5}} + C

Solution steps

\int e^{\frac{2 x}{5}} d x

Apply u-substitution

: \int e^{u} \frac{5}{2} d u

= \int e^{u} \frac{5}{2} d u

Take the constant out:

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

= \frac{5}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{5}{2} e^{u}

Substitute back

u = \frac{2 x}{5}

= \frac{5}{2} e^{\frac{2 x}{5}}

Add a constant to the solution

= \frac{5}{2} e^{\frac{2 x}{5}} + C

\frac{1}{1 - x}, 20

\int 6 x y d x

\frac{d y}{d x}, (4 x + 4 y) 3 = 64 x^{3} + 64 y^{3}

f (x) = - 3 - 5 x^{2}, at x = 3

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

What is the integral of e^{(2x)/5} ?
The integral of e^{(2x)/5} is 5/2 e^{(2x)/5}+C