What is the integral of e^xx^5 ?

The integral of e^xx^5 is x^5e^x-5(x^4e^x-4(x^3e^x-3(x^2e^x-2(e^xx-e^x))))+C

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integral of e^xx^5

\int e^{x} x^{5} d x

x^{5} e^{x} - 5 (x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))) + C

Solution steps

\int e^{x} x^{5} d x

Apply Integration By Parts

: x^{5} e^{x} - \int 5 x^{4} e^{x} d x

= x^{5} e^{x} - \int 5 x^{4} e^{x} d x

\int 5 x^{4} e^{x} d x = 5 (x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))))

= x^{5} e^{x} - 5 (x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))))

Add a constant to the solution

= x^{5} e^{x} - 5 (x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))) + C

x \to 1 - lim (\frac{1}{2} ln (x^{2} - 1))

\frac{1}{( s ( s + 1 ) )}

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

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2}})

\int_{0}^{1} (3 x - 1)^{50} d x

What is the integral of e^xx^5 ?
The integral of e^xx^5 is x^5e^x-5(x^4e^x-4(x^3e^x-3(x^2e^x-2(e^xx-e^x))))+C