What is the integral of (-3)/(sqrt(2t+3)) ?

The integral of (-3)/(sqrt(2t+3)) is -3sqrt(2t+3)+C

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integral of (-3)/(sqrt(2t+3))

\int \frac{- 3}{2 t + 3} d t

- 3 2 t + 3 + C

Solution steps

\int \frac{- 3}{2 t + 3} d t

Take the constant out:

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

= - 3 \cdot \int \frac{1}{2 t + 3} d t

Apply u-substitution

: \int \frac{1}{2 u} d u

= - 3 \cdot \int \frac{1}{2 u} d u

Take the constant out:

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

= - 3 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - 3 \cdot \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 2 t + 3

= - 3 \cdot \frac{1}{2} \cdot 2 (2 t + 3)^{\frac{1}{2}}

Simplify

- 3 \cdot \frac{1}{2} \cdot 2 (2 t + 3)^{\frac{1}{2}} : - 3 2 t + 3

= - 3 2 t + 3

Add a constant to the solution

= - 3 2 t + 3 + C

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What is the integral of (-3)/(sqrt(2t+3)) ?
The integral of (-3)/(sqrt(2t+3)) is -3sqrt(2t+3)+C