What is the integral of (x^{3/2}+2x^6+1.2)/x ?

The integral of (x^{3/2}+2x^6+1.2)/x is 0.66666…x^{3/2}+0.33333…x^6+1.2ln|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^{3/2}+2x^6+1.2)/x

\int \frac{x ^{\frac{3}{2}} + 2 x ^{6} + 1.2}{x} d x

0.66666 \dots x^{\frac{3}{2}} + 0.33333 \dots x^{6} + 1.2 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{\frac{3}{2}} + 2 x ^{6} + 1.2}{x} d x

Expand

\frac{x ^{\frac{3}{2}} + 2 x ^{6} + 1.2}{x} : x^{\frac{1}{2}} + 2 x^{5} + \frac{1.2}{x}

= \int x^{\frac{1}{2}} + 2 x^{5} + \frac{1.2}{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 x^{\frac{1}{2}} d x + \int 2 x^{5} d x + \int \frac{1.2}{x} d x

\int x^{\frac{1}{2}} d x = \frac{2}{3} x^{\frac{3}{2}}

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

\int \frac{1.2}{x} d x = 1.2 ln ∣ x ∣

= \frac{2}{3} x^{\frac{3}{2}} + \frac{x ^{6}}{3} + 1.2 ln ∣ x ∣

Simplify

= 0.66666 \dots x^{\frac{3}{2}} + 0.33333 \dots x^{6} + 1.2 ln ∣ x ∣

Add a constant to the solution

= 0.66666 \dots x^{\frac{3}{2}} + 0.33333 \dots x^{6} + 1.2 ln ∣ x ∣ + C

cos (arctan (3 x) - arcsin (2 x))

\frac{d}{d x} (6 \cdot 5^{x})

\frac{d}{d x} (sin (tan (1 + x^{3})))

\frac{d x}{d y} = 1 + x^{2}

\int \frac{e ^{- x}}{1 - e ^{- x}} d x

What is the integral of (x^{3/2}+2x^6+1.2)/x ?
The integral of (x^{3/2}+2x^6+1.2)/x is 0.66666…x^{3/2}+0.33333…x^6+1.2ln|x|+C