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

The integral of ((x^2)/3-3/(2x-3)-e^{3x}) is (x^3)/9-3/2 ln|2x-3|-1/3 e^{3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ((x^2)/3-3/(2x-3)-e^{3x})

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

\frac{x ^{3}}{9} - \frac{3}{2} ln ∣ 2 x - 3 ∣ - \frac{1}{3} e^{3 x} + C

Solution steps

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

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

\int \frac{3}{2 x - 3} d x = \frac{3}{2} ln ∣ 2 x - 3 ∣

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= \frac{x ^{3}}{9} - \frac{3}{2} ln ∣ 2 x - 3 ∣ - \frac{1}{3} e^{3 x}

Add a constant to the solution

= \frac{x ^{3}}{9} - \frac{3}{2} ln ∣ 2 x - 3 ∣ - \frac{1}{3} e^{3 x} + C

What is the integral of ((x^2)/3-3/(2x-3)-e^{3x}) ?
The integral of ((x^2)/3-3/(2x-3)-e^{3x}) is (x^3)/9-3/2 ln|2x-3|-1/3 e^{3x}+C