What is the integral of-4x^6e^x ?

The integral of-4x^6e^x is -4(x^6e^x-6(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-4x^6e^x

\int - 4 x^{6} e^{x} d x

- 4 (x^{6} e^{x} - 6 (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 - 4 x^{6} e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 4 \cdot \int x^{6} e^{x} d x

Apply Integration By Parts

: x^{6} e^{x} - \int 6 x^{5} e^{x} d x

= - 4 (x^{6} e^{x} - \int 6 x^{5} e^{x} d x)

\int 6 x^{5} e^{x} d x = 6 (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})))))

= - 4 (x^{6} e^{x} - 6 (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

= - 4 (x^{6} e^{x} - 6 (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 (2 + 5 x)^{2} d x

\int (x + 2) d x

3 x e^{- a x}

5 t^{2} y^{^{''}} + t y^{^{'}} - 12 y = 0

\int \frac{x ^{2}}{x ^{6} - 9} d x

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