What is the integral from 0 to 4 of 2/(sqrt(2x+1)) ?

The integral from 0 to 4 of 2/(sqrt(2x+1)) is 4

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integral from 0 to 4 of 2/(sqrt(2x+1))

\int_{0}^{4} \frac{2}{2 x + 1} d x

4

Solution steps

\int_{0}^{4} \frac{2}{2 x + 1} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{4} \frac{1}{2 x + 1} d x

Apply u-substitution

: \int_{1}^{3} 1 d u

= 2 \cdot \int_{1}^{3} 1 d u

Integral of a constant:

\int a d x = a x

= 2 [1 \cdot u]_{1}^{3}

Simplify

= 2 [u]_{1}^{3}

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4

\int_{0}^{1} (2 - y)^{2} y d y

\int_{0}^{2} 4 x (x^{2} + 3)^{3} d x

\int_{2}^{3} (x^{2} - 2 x - 15) d x

\int_{0}^{2} \frac{1}{( x - 1 )} d x

\int_{- 3}^{3} (x^{2} + x + 1) d x

What is the integral from 0 to 4 of 2/(sqrt(2x+1)) ?
The integral from 0 to 4 of 2/(sqrt(2x+1)) is 4