What is the integral of 5.4sqrt(-3x+4) ?

The integral of 5.4sqrt(-3x+4) is -1.2(-3x+4)^{3/2}+C

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integral of 5.4sqrt(-3x+4)

\int 5.4 - 3 x + 4 d x

- 1.2 (- 3 x + 4)^{\frac{3}{2}} + C

Solution steps

\int 5.4 - 3 x + 4 d x

Take the constant out:

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

= 5.4 \cdot \int - 3 x + 4 d x

Apply u-substitution

: \int - \frac{u}{3} d u

= 5.4 \cdot \int - \frac{u}{3} d u

Take the constant out:

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

= 5.4 (- \frac{1}{3} \cdot \int u d u)

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= 5.4 (- \frac{1}{3} \cdot \frac{2}{3} u^{\frac{3}{2}})

Substitute back

u = - 3 x + 4

= 5.4 (- \frac{1}{3} \cdot \frac{2}{3} (- 3 x + 4)^{\frac{3}{2}})

Simplify

5.4 (- \frac{1}{3} \cdot \frac{2}{3} (- 3 x + 4)^{\frac{3}{2}}) : - 1.2 (- 3 x + 4)^{\frac{3}{2}}

= - 1.2 (- 3 x + 4)^{\frac{3}{2}}

Add a constant to the solution

= - 1.2 (- 3 x + 4)^{\frac{3}{2}} + C

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What is the integral of 5.4sqrt(-3x+4) ?
The integral of 5.4sqrt(-3x+4) is -1.2(-3x+4)^{3/2}+C