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

\frac{d y}{d x} + 3 x^{2} y = 6 x^{2}

(- 4, - 5), (3, - 5)

\int \frac{sin ( x )}{4 + cos ^{2} ( x )} d x

\int (5 + 2 w^{3} - w^{5}) cos (3 w) d w

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

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