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Popular >

integral of (1/5)^x

Solution

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

Solution

- \frac{1}{ln ( 5 ) \cdot 5 ^{x}} + C

Solution steps

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

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(arcsin(6xyz))

\frac{\partial}{\partial x} (arcsin (6 x yz))

derivative of (3t+4)*sin(pi(t/3-0.5))derivative of

(3 t + 4) \cdot sin (π (\frac{t}{3} - 0.5))

y^{''}-y^'-12y=-5,y(0)=0,y^'(0)=0

y^{^{''}} - y^{^{'}} - 12 y = - 5, y (0) = 0, y^{^{'}} (0) = 0

limit as x approaches 2-of x/(2-x)

x \to 2 - lim (\frac{x}{2 - x})

integral of (x^2)/(sqrt(289-x^2))

\int \frac{x ^{2}}{289 - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (1/5)^x ?
The integral of (1/5)^x is -1/(ln(5)*5^x)+C