What is the integral of sqrt(5^x) ?

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

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integral of sqrt(5^x)

\int 5^{x} d x

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

Solution steps

\int 5^{x} d x

Apply Integration By Parts

= 5^{\frac{x}{2}} x - \int \frac{1}{2} ln (5) \cdot 5^{\frac{x}{2}} x d x

\int \frac{1}{2} ln (5) \cdot 5^{\frac{x}{2}} x d x = 5^{\frac{x}{2}} x - \frac{2 \cdot 5 ^{\frac{x}{2}}}{ln ( 5 )}

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

Simplify

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

Add a constant to the solution

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

\frac{d y}{d x} = 0.5 y - 450

d er i v a t i v e 2 x cos (x)

\int \frac{1}{4 + ( x - 3 ) ^{2}} d x

\int (sin (π x)) d x

\frac{\partial}{\partial y} (5 z e^{x yz})

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