What is the integral of (5^x)/(ln(5)) ?

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

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integral of (5^x)/(ln(5))

\int \frac{5 ^{x}}{ln ( 5 )} d x

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

Solution steps

\int \frac{5 ^{x}}{ln ( 5 )} d x

Take the constant out:

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

x \to \infty lim (20)

y = \frac{1}{x ^{2}}, (- 2, \frac{1}{4})

x \to - \infty lim (3^{5 x})

\int \frac{sin ^{3} ( x )}{cos ^{6} ( x )} d x

y = 3 + 4 x^{2} - 2 x^{3}, at x = a

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