What is the integral of (x^3e^x-8x^2)/(x^3) ?

The integral of (x^3e^x-8x^2)/(x^3) is e^x-8ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^3e^x-8x^2)/(x^3)

\int \frac{x ^{3} e ^{x} - 8 x ^{2}}{x ^{3}} d x

e^{x} - 8 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{3} e ^{x} - 8 x ^{2}}{x ^{3}} d x

Expand

\frac{x ^{3} e ^{x} - 8 x ^{2}}{x ^{3}} : e^{x} - \frac{8}{x}

= \int e^{x} - \frac{8}{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{8}{x} d x

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

\int \frac{8}{x} d x = 8 ln ∣ x ∣

= e^{x} - 8 ln ∣ x ∣

Add a constant to the solution

= e^{x} - 8 ln ∣ x ∣ + C

\int 6 sin (3 (x - 2)) d x

\int x^{2} (3 x + 2) d x

\int 14 x^{2} d x

\int 1 + cos (4 θ) d θ

\int \frac{6 x ^{2}}{( 1 - 4 x ^{3} ) ^{4}} d x

What is the integral of (x^3e^x-8x^2)/(x^3) ?
The integral of (x^3e^x-8x^2)/(x^3) is e^x-8ln|x|+C