What is the integral of 2/(3x)+2x^5 ?

The integral of 2/(3x)+2x^5 is 2/3 ln|x|+(x^6)/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(3x)+2x^5

\int \frac{2}{3 x} + 2 x^{5} d x

\frac{2}{3} ln ∣ x ∣ + \frac{x ^{6}}{3} + C

Solution steps

\int \frac{2}{3 x} + 2 x^{5} 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{2}{3 x} d x + \int 2 x^{5} d x

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

\int 2 x^{5} d x = \frac{x ^{6}}{3}

= \frac{2}{3} ln ∣ x ∣ + \frac{x ^{6}}{3}

Add a constant to the solution

= \frac{2}{3} ln ∣ x ∣ + \frac{x ^{6}}{3} + C

\int \frac{t ^{2} ( t ^{2} + 6 )}{( t ^{2} + 2 ) ^{2}} d t

\int 2 x cos (x^{2} - 1) d x

\int \frac{1}{( x - 1 ) ^{2} \cdot ( x ^{2} + 3 )} d x

\int p (p + 4)^{7} d p

\int \frac{1}{u ^{8}} d u

What is the integral of 2/(3x)+2x^5 ?
The integral of 2/(3x)+2x^5 is 2/3 ln|x|+(x^6)/3+C