What is the integral of (x^4e^x-4x^3)/(x^4) ?

The integral of (x^4e^x-4x^3)/(x^4) is e^x-4ln|x|+C

Popular >

integral of (x^4e^x-4x^3)/(x^4)

\int \frac{x ^{4} e ^{x} - 4 x ^{3}}{x ^{4}} d x

e^{x} - 4 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{4} e ^{x} - 4 x ^{3}}{x ^{4}} d x

Expand

\frac{x ^{4} e ^{x} - 4 x ^{3}}{x ^{4}} : e^{x} - \frac{4}{x}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= e^{x} - 4 ln ∣ x ∣

Add a constant to the solution

= e^{x} - 4 ln ∣ x ∣ + C

y^{^{'}} = 9.8 - 0.2 y, y (0) = 100

n = - 4 \sum \infty (- \frac{4}{9})^{n}

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

y^{^{'}} = - \frac{y}{2000} 4

What is the integral of (x^4e^x-4x^3)/(x^4) ?
The integral of (x^4e^x-4x^3)/(x^4) is e^x-4ln|x|+C