What is the integral of |u+1| ?

The integral of |u+1| is ((u+1)|u+1|)/2+C

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integral of |u+1|

\int ∣ u + 1 ∣ d u

\frac{( u + 1 ) ∣ u + 1 ∣}{2} + C

Solution steps

\int ∣ u + 1 ∣ d u

Apply u-substitution

: \int ∣ v ∣ d v

= \int ∣ v ∣ d v

Use the common integral:

\int ∣ v ∣ d v = \frac{v ∣ v ∣}{2}

= \frac{v ∣ v ∣}{2}

Substitute back

v = u + 1

= \frac{( u + 1 ) ∣ u + 1 ∣}{2}

Add a constant to the solution

= \frac{( u + 1 ) ∣ u + 1 ∣}{2} + C

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