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Popular >

integral of 5^xln(5)

Solution

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

Solution

5^{x} + C

Solution steps

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

Take the constant out:

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

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

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

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

Simplify

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

= 5^{x}

Add a constant to the solution

= 5^{x} + C

Popular Examples

integral from-pi to pi of cos^2(3x)

\int_{- π}^{π} cos^{2} (3 x) d x

integral from-1 to 22 of 21x-(x^2-22)

\int_{- 1}^{22} 21 x - (x^{2} - 22) d x

integral of 4x+2

\int 4 x + 2 d x

derivative of 1/2 e^{x^2}

\frac{d}{d x} (\frac{1}{2} e^{x^{2}})

derivative of (x^2)/(5(1-x))derivative of

\frac{x ^{2}}{5 ( 1 - x )}

Frequently Asked Questions (FAQ)

What is the integral of 5^xln(5) ?
The integral of 5^xln(5) is 5^x+C