What is the integral of ((x^6e^x))/x ?

The integral of ((x^6e^x))/x 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 ((x^6e^x))/x

\int \frac{( x ^{6} e ^{x} )}{x} 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 \frac{x ^{6} e ^{x}}{x} d x

Cancel the common factor:

x

= \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

\int (1 - x) x^{3} (x - 2)^{2} d x

x y^{^{'}} - 2 y = 2 x^{2} - 2 x - 2

\frac{d}{d x} (5 x^{0.5})

6 x + 9

\int \frac{e ^{x} - 1}{e ^{x} + 1} d x

What is the integral of ((x^6e^x))/x ?
The integral of ((x^6e^x))/x is x^5e^x-5(x^4e^x-4(x^3e^x-3(x^2e^x-2(e^xx-e^x))))+C