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Popular >

integral of |2x|

Solution

\int ∣ 2 x ∣ d x

Solution

x ∣ x ∣ + C

Solution steps

\int ∣ 2 x ∣ d x

Apply absolute rule:

∣ a x ∣ = a ∣ x ∣, a \geq 0

= \int 2 ∣ x ∣ d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int ∣ x ∣ d x

Use the common integral:

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 2 \cdot \frac{x ∣ x ∣}{2}

Simplify

2 \cdot \frac{x ∣ x ∣}{2} : x ∣ x ∣

= x ∣ x ∣

Add a constant to the solution

= x ∣ x ∣ + C

Popular Examples

tangent of f(x)=3x^5e^{2x}tangent of

f (x) = 3 x^{5} e^{2 x}

limit as x approaches 0 of 1/(x+1)-1

x \to 0 lim (\frac{1}{x + 1} - 1)

derivative of e^{-0.5}(2x+1)^{0.5}derivative of

e^{- 0.5} (2 x + 1)^{0.5}

integral of cos^3(xsi)n^5x

\int cos^{3} (x s i) n^{5} x d x

y^{''}+25y=cos(2t)

y^{^{''}} + 25 y = cos (2 t)

Frequently Asked Questions (FAQ)

What is the integral of |2x| ?
The integral of |2x| is x|x|+C