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

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

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integral of 2^{x/5}

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

\frac{5 \cdot 2 ^{\frac{x}{5}}}{ln ( 2 )} + C

Solution steps

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

Apply u-substitution

: \int 2^{u} \cdot 5 d u

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

Take the constant out:

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

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

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 5 \cdot \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = \frac{x}{5}

= 5 \cdot \frac{2 ^{\frac{x}{5}}}{ln ( 2 )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 \cdot 2 ^{\frac{x}{5}}}{ln ( 2 )}

Add a constant to the solution

= \frac{5 \cdot 2 ^{\frac{x}{5}}}{ln ( 2 )} + C

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