What is the integral of 5/(sqrt(2x+1)) ?

The integral of 5/(sqrt(2x+1)) is 5sqrt(2x+1)+C

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integral of 5/(sqrt(2x+1))

\int \frac{5}{2 x + 1} d x

5 2 x + 1 + C

Solution steps

\int \frac{5}{2 x + 1} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{2 x + 1} d x

Apply u-substitution

: \int 1 d u

= 5 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 5 \cdot 1 \cdot u

Substitute back

u = 2 x + 1

= 5 \cdot 1 \cdot 2 x + 1

Simplify

= 5 2 x + 1

Add a constant to the solution

= 5 2 x + 1 + C

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What is the integral of 5/(sqrt(2x+1)) ?
The integral of 5/(sqrt(2x+1)) is 5sqrt(2x+1)+C