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

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

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integral of 2^{5x+2}

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

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

Solution steps

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

Apply u-substitution

= \int 2^{u} \cdot \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int 2^{u} d u

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

= \frac{1}{5} \cdot \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = 5 x + 2

= \frac{1}{5} \cdot \frac{2 ^{5 x + 2}}{ln ( 2 )}

Simplify

\frac{1}{5} \cdot \frac{2 ^{5 x + 2}}{ln ( 2 )} : \frac{2 ^{5 x + 2}}{5 ln ( 2 )}

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

Add a constant to the solution

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

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