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Popular >

integral of x-4|x|

Solution

\int x - 4 ∣ x ∣ d x

Solution

\frac{x ^{2}}{2} - 2 x ∣ x ∣ + C

Solution steps

\int x - 4 ∣ 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 d x - \int 4 ∣ x ∣ d x

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

\int 4 ∣ x ∣ d x = 2 x ∣ x ∣

= \frac{x ^{2}}{2} - 2 x ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - 2 x ∣ x ∣ + C

Popular Examples

integral of 12x+2

\int 12 x + 2 d x

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

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

integral of 2-5/(x^2)

\int 2 - \frac{5}{x ^{2}} d x

integral of 5x^2e^{-3x}

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

integral of tan(x)sec^2(x)integral

tan (x) sec^{2} (x)

Frequently Asked Questions (FAQ)

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