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

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

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integral of 5^{x+2}

\int 5^{x + 2} d x

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

Solution steps

\int 5^{x + 2} d x

Simplify

5^{x + 2} : 5^{x} \cdot 5^{2}

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

Take the constant out:

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

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

Simplify

= 25 \cdot \int 5^{x} d x

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

= 25 \cdot \frac{5 ^{x}}{ln ( 5 )}

Simplify

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

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

Add a constant to the solution

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

\frac{d}{d x} ((x^{3} + 3)^{2})

(1, 3), (3, - 2)

\int - cos (t) - sin (t) d t

\frac{d}{d x} (\frac{cos ( 5 ) x ^{2}}{x ^{2}})

\int (3 + tan^{2} (x)) d x

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