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Popular >

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

Solution

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

Solution

2 x^{2} - x + C

Solution steps

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

Expand

\frac{4 x ^{2} - x}{x} : \frac{4 x ^{2}}{x} - \frac{x}{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{4 x ^{2}}{x} d x - \int \frac{x}{x} d x

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

\int \frac{x}{x} d x = x

= 2 x^{2} - x

Add a constant to the solution

= 2 x^{2} - x + C

Popular Examples

integral of 1/(g-kv^2)

\int \frac{1}{g - k v ^{2}} d v

integral of (x^2)/(sqrt(x^2+y^2))

\int \frac{x ^{2}}{x ^{2} + y ^{2}} d x

integral of (\partial)/(\partial x)(x^2)

\int \frac{\partial}{\partial x} (x^{2}) d x

integral of tan^2(1-x)

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

integral of (-2x^{-3}+20x^{-5})

\int (- 2 x^{- 3} + 20 x^{- 5}) d x

Frequently Asked Questions (FAQ)

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