What is the integral of x6^x ?

The integral of x6^x is (6^xx)/(ln(6))-(6^x)/(ln^2(6))+C

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integral of x6^x

\int x 6^{x} d x

\frac{6 ^{x} x}{ln ( 6 )} - \frac{6 ^{x}}{ln ^{2} ( 6 )} + C

Solution steps

\int x \cdot 6^{x} d x

Apply Integration By Parts

: \frac{6 ^{x} x}{ln ( 6 )} - \int \frac{6 ^{x}}{ln ( 6 )} d x

= \frac{6 ^{x} x}{ln ( 6 )} - \int \frac{6 ^{x}}{ln ( 6 )} d x

\int \frac{6 ^{x}}{ln ( 6 )} d x = \frac{6 ^{x}}{ln ^{2} ( 6 )}

= \frac{6 ^{x} x}{ln ( 6 )} - \frac{6 ^{x}}{ln ^{2} ( 6 )}

Add a constant to the solution

= \frac{6 ^{x} x}{ln ( 6 )} - \frac{6 ^{x}}{ln ^{2} ( 6 )} + C

x \to 9 + lim (\frac{5 x}{x - 9})

\int (- 2 x) d x

\frac{d ^{4}}{d x ^{4}} (\frac{1}{1 + x})

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

f (x) = \frac{x ^{2} - 3 x}{x + 1}

What is the integral of x6^x ?
The integral of x6^x is (6^xx)/(ln(6))-(6^x)/(ln^2(6))+C