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Popular Calculus >

integral of (5/4)^x

Solution

\int (\frac{5}{4})^{x} d x

Solution

\frac{5 ^{x}}{ln ( \frac{5}{4} ) \cdot 4 ^{x}} + C

Solution steps

\int (\frac{5}{4})^{x} d x

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

= \frac{( \frac{5}{4} ) ^{x}}{ln ( \frac{5}{4} )}

Simplify

\frac{( \frac{5}{4} ) ^{x}}{ln ( \frac{5}{4} )} : \frac{5 ^{x}}{ln ( \frac{5}{4} ) \cdot 4 ^{x}}

= \frac{5 ^{x}}{ln ( \frac{5}{4} ) \cdot 4 ^{x}}

Add a constant to the solution

= \frac{5 ^{x}}{ln ( \frac{5}{4} ) \cdot 4 ^{x}} + C

Graph

Popular Examples

integral of 8x^3-5x^{1/3}+4

\int 8 x^{3} - 5 x^{\frac{1}{3}} + 4 d x

integral of (x+8)sqrt(16x+x^2)

\int (x + 8) 16 x + x^{2} d x

integral of (x^3-3x^2+4x-1)/(3x)

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

integral of (x^3+2)^2

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

integral of (2xsqrt(x)-5x-2)

\int (2 x x - 5 x - 2) d x

Frequently Asked Questions (FAQ)

What is the integral of (5/4)^x ?
The integral of (5/4)^x is (5^x)/(ln(5/4)*4^x)+C