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Popular >

integral of (|x|+1)

Solution

\int (∣ x ∣ + 1) d x

Solution

\frac{x ∣ x ∣}{2} + x + C

Solution steps

\int ∣ x ∣ + 1 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 1 d x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

\int 1 d x = x

= \frac{x ∣ x ∣}{2} + x

Add a constant to the solution

= \frac{x ∣ x ∣}{2} + x + C

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Frequently Asked Questions (FAQ)

What is the integral of (|x|+1) ?
The integral of (|x|+1) is (x|x|)/2+x+C