What is the integral of e^{(2x)/3} ?

The integral of e^{(2x)/3} is 3/2 e^{(2x)/3}+C

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integral of e^{(2x)/3}

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

\frac{3}{2} e^{\frac{2 x}{3}} + C

Solution steps

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

Apply u-substitution

: \int e^{u} \frac{3}{2} d u

= \int e^{u} \frac{3}{2} d u

Take the constant out:

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

= \frac{3}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{3}{2} e^{u}

Substitute back

u = \frac{2 x}{3}

= \frac{3}{2} e^{\frac{2 x}{3}}

Add a constant to the solution

= \frac{3}{2} e^{\frac{2 x}{3}} + C

\int_{0}^{1} \frac{x ^{2}}{e ^{x}} d x

x \to 2 lim (\frac{5}{( x - 5 ) ^{2}})

3 y^{^{''}} - 6 y^{^{'}} + 6 y = 0

- x^{2} - 2 x + 9, [- 4, 0]

What is the integral of e^{(2x)/3} ?
The integral of e^{(2x)/3} is 3/2 e^{(2x)/3}+C