What is the integral of 2^{3x+1} ?

The integral of 2^{3x+1} is (2^{3x+1})/(3ln(2))+C

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integral of 2^{3x+1}

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

\frac{2 ^{3 x + 1}}{3 ln ( 2 )} + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

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

= \frac{1}{3} \cdot \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = 3 x + 1

= \frac{1}{3} \cdot \frac{2 ^{3 x + 1}}{ln ( 2 )}

Simplify

\frac{1}{3} \cdot \frac{2 ^{3 x + 1}}{ln ( 2 )} : \frac{2 ^{3 x + 1}}{3 ln ( 2 )}

= \frac{2 ^{3 x + 1}}{3 ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{3 x + 1}}{3 ln ( 2 )} + C

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What is the integral of 2^{3x+1} ?
The integral of 2^{3x+1} is (2^{3x+1})/(3ln(2))+C