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

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

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

\int e^{\frac{2 x}{π}} d x

\frac{π}{2} e^{\frac{2 x}{π}} + C

Solution steps

\int e^{\frac{2 x}{π}} d x

Apply u-substitution

: \int e^{u} \frac{π}{2} d u

= \int e^{u} \frac{π}{2} d u

Take the constant out:

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

= \frac{π}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{π}{2} e^{u}

Substitute back

u = \frac{2 x}{π}

= \frac{π}{2} e^{\frac{2 x}{π}}

Add a constant to the solution

= \frac{π}{2} e^{\frac{2 x}{π}} + C

\int \frac{( x + 1 )}{x ^{2} + 5 x + 6} d x

1 - 3 x

\int \frac{tan ( ln ( 2 x + 4 ) )}{2 x + 4} d x

4 x + 1

\frac{d}{d x} (1 - x^{\frac{3}{2}})

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