What is the integral of (2x^3-1/(x^4)) ?

The integral of (2x^3-1/(x^4)) is (x^4)/2+1/(3x^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^3-1/(x^4))

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

\frac{x ^{4}}{2} + \frac{1}{3 x ^{3}} + C

Solution steps

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int \frac{1}{x ^{4}} d x = - \frac{1}{3 x ^{3}}

= \frac{x ^{4}}{2} - (- \frac{1}{3 x ^{3}})

Simplify

= \frac{x ^{4}}{2} + \frac{1}{3 x ^{3}}

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{1}{3 x ^{3}} + C

\int \frac{e ^{3 x} + 5 e ^{2 x} - 4 e ^{x}}{e ^{x}} d x

\int 3 x (2 x + 5)^{2} d x

\int \frac{( 7 x + 1 )}{x ^{2} - 7 x + 6} d x

\int (sec^{2} (x) tan^{3} (x)) d x

\int e^{- 0.0025 x} d x

What is the integral of (2x^3-1/(x^4)) ?
The integral of (2x^3-1/(x^4)) is (x^4)/2+1/(3x^3)+C