What is the integral of x10^x ?

The integral of x10^x is (10^xx)/(ln(10))-(10^x)/(ln^2(10))+C

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integral of x10^x

\int x 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

(\frac{9 y ^{2} - t ^{2}}{y ^{5}}) \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

x^{2} - 2 x + 4, 2

\int_{0}^{1} \frac{1}{1 - x} d x

P (x) = x^{3} - 2 x^{2} + 2 x - 1

\int_{0}^{1} x x^{2} + 8 d x

What is the integral of x10^x ?
The integral of x10^x is (10^xx)/(ln(10))-(10^x)/(ln^2(10))+C