What is the integral of ((x^3+3x^6))/(x^4) ?

The integral of ((x^3+3x^6))/(x^4) is ln|x|+x^3+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+3x^6))/(x^4)

\int \frac{( x ^{3} + 3 x ^{6} )}{x ^{4}} d x

ln ∣ x ∣ + x^{3} + C

Solution steps

\int \frac{x ^{3} + 3 x ^{6}}{x ^{4}} d x

Expand

\frac{x ^{3} + 3 x ^{6}}{x ^{4}} : \frac{1}{x} + 3 x^{2}

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ + x^{3}

Add a constant to the solution

= ln ∣ x ∣ + x^{3} + C

\int 7 x x^{2} + 1 d x

\int cos (5 t) + t^{4} d t

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

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

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

What is the integral of ((x^3+3x^6))/(x^4) ?
The integral of ((x^3+3x^6))/(x^4) is ln|x|+x^3+C