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Popular >

integral of x+|x|

Solution

\int x + ∣ x ∣ d x

Solution

\frac{x ^{2}}{2} + \frac{x ∣ x ∣}{2} + C

Solution steps

\int x + ∣ 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 ∣ x ∣ d x

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

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= \frac{x ^{2}}{2} + \frac{x ∣ x ∣}{2}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{x ∣ x ∣}{2} + C

Popular Examples

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\int \frac{1}{x ln ( 5 x )} d x

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

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2 y^{3}

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\int (x^{3} - a^{3})^{5} d x

integral of-8cos(t)

\int - 8 cos (t) d t

Frequently Asked Questions (FAQ)

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