What is the integral of 3sqrt(4x-7) ?

The integral of 3sqrt(4x-7) is 1/2 (4x-7)^{3/2}+C

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integral of 3sqrt(4x-7)

\int 3 4 x - 7 d x

\frac{1}{2} (4 x - 7)^{\frac{3}{2}} + C

Solution steps

\int 3 4 x - 7 d x

Take the constant out:

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

= 3 \cdot \int 4 x - 7 d x

Apply u-substitution

= 3 \cdot \int \frac{u}{4} d u

Take the constant out:

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

= 3 \cdot \frac{1}{4} \cdot \int u d u

Apply the Power Rule

= 3 \cdot \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 4 x - 7

= 3 \cdot \frac{1}{4} \cdot \frac{2}{3} (4 x - 7)^{\frac{3}{2}}

Simplify

3 \cdot \frac{1}{4} \cdot \frac{2}{3} (4 x - 7)^{\frac{3}{2}} : \frac{1}{2} (4 x - 7)^{\frac{3}{2}}

= \frac{1}{2} (4 x - 7)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{2} (4 x - 7)^{\frac{3}{2}} + C

What is the integral of 3sqrt(4x-7) ?
The integral of 3sqrt(4x-7) is 1/2 (4x-7)^{3/2}+C