What is the integral of x*10^x ?

The integral of x*10^x is (10^xx)/(ln(10))-(10^x)/(ln^2(10))+C

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integral of x*10^x

\int x \cdot 1 0^{x} d x

\frac{1 0 ^{x} x}{ln ( 10 )} - \frac{1 0 ^{x}}{ln ^{2} ( 10 )} + C

Solution steps

\int x \cdot 1 0^{x} d x

Apply Integration By Parts

: \frac{1 0 ^{x} x}{ln ( 10 )} - \int \frac{1 0 ^{x}}{ln ( 10 )} d x

= \frac{1 0 ^{x} x}{ln ( 10 )} - \int \frac{1 0 ^{x}}{ln ( 10 )} d x

\int \frac{1 0 ^{x}}{ln ( 10 )} d x = \frac{1 0 ^{x}}{ln ^{2} ( 10 )}

= \frac{1 0 ^{x} x}{ln ( 10 )} - \frac{1 0 ^{x}}{ln ^{2} ( 10 )}

Add a constant to the solution

= \frac{1 0 ^{x} x}{ln ( 10 )} - \frac{1 0 ^{x}}{ln ^{2} ( 10 )} + C

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What is the integral of x*10^x ?
The integral of x*10^x is (10^xx)/(ln(10))-(10^x)/(ln^2(10))+C