What is the integral of (e^{(2q-5)/3}) ?

The integral of (e^{(2q-5)/3}) is 3/2 e^{1/3 (2q-5)}+C

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integral of (e^{(2q-5)/3})

\int (e^{\frac{2 q - 5}{3}}) d q

\frac{3}{2} e^{\frac{1}{3} (2 q - 5)} + C

Solution steps

\int e^{\frac{2 q - 5}{3}} d q

Apply u-substitution

: \int e^{\frac{u}{3}} \frac{1}{2} d u

= \int e^{\frac{u}{3}} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{\frac{u}{3}} d u

Apply u-substitution

: \int e^{v} \cdot 3 d v

= \frac{1}{2} \cdot \int e^{v} \cdot 3 d v

Take the constant out:

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

= \frac{1}{2} \cdot 3 \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{2} \cdot 3 e^{v}

Substitute back

= \frac{1}{2} \cdot 3 e^{\frac{2 q - 5}{3}}

Simplify

\frac{1}{2} \cdot 3 e^{\frac{2 q - 5}{3}} : \frac{3}{2} e^{\frac{1}{3} (2 q - 5)}

= \frac{3}{2} e^{\frac{1}{3} (2 q - 5)}

Add a constant to the solution

= \frac{3}{2} e^{\frac{1}{3} (2 q - 5)} + C

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What is the integral of (e^{(2q-5)/3}) ?
The integral of (e^{(2q-5)/3}) is 3/2 e^{1/3 (2q-5)}+C