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Popular >

integral of (x-2|x|)

Solution

\int (x - 2 ∣ x ∣) d x

Solution

\frac{x ^{2}}{2} - x ∣ x ∣ + C

Solution steps

\int x - 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 d x - \int 2 ∣ x ∣ d x

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

\int 2 ∣ x ∣ d x = x ∣ x ∣

= \frac{x ^{2}}{2} - x ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - x ∣ x ∣ + C

Popular Examples

integral of 8/((y-9)^3)

\int \frac{8}{( y - 9 ) ^{3}} d y

integral of 2x*ln(x)

\int 2 x \cdot ln (x) d x

integral of 2x^2+\sqrt[3]{x}-1

integral of 2-2y

\int 2 - 2 y d y

integral of (3-x)/((3x+1)(x-1))

\int \frac{3 - x}{( 3 x + 1 ) ( x - 1 )} d x

Frequently Asked Questions (FAQ)

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