What is the integral of 15(3x-7)^{3/2} ?

The integral of 15(3x-7)^{3/2} is 2(3x-7)^{5/2}+C

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integral of 15(3x-7)^{3/2}

\int 15 (3 x - 7)^{\frac{3}{2}} d x

2 (3 x - 7)^{\frac{5}{2}} + C

Solution steps

\int 15 (3 x - 7)^{\frac{3}{2}} d x

Take the constant out:

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

= 15 \cdot \int (3 x - 7)^{\frac{3}{2}} d x

Apply u-substitution

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

= 15 \cdot \int \frac{u ^{\frac{3}{2}}}{3} d u

Take the constant out:

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

= 15 \cdot \frac{1}{3} \cdot \int u^{\frac{3}{2}} d u

Apply the Power Rule

: \frac{2}{5} u^{\frac{5}{2}}

= 15 \cdot \frac{1}{3} \cdot \frac{2}{5} u^{\frac{5}{2}}

Substitute back

u = 3 x - 7

= 15 \cdot \frac{1}{3} \cdot \frac{2}{5} (3 x - 7)^{\frac{5}{2}}

Simplify

15 \cdot \frac{1}{3} \cdot \frac{2}{5} (3 x - 7)^{\frac{5}{2}} : 2 (3 x - 7)^{\frac{5}{2}}

= 2 (3 x - 7)^{\frac{5}{2}}

Add a constant to the solution

= 2 (3 x - 7)^{\frac{5}{2}} + C

\frac{d}{d x} (2 e^{x} - 3 x^{e} + e)

x \to 0 lim (\frac{2 + sin ( x )}{x})

\int 2 x + 5 d x

x \frac{d y}{d x} + y = 4 x + 1, y (1) = 8

x \to 6 lim (x - 5)

What is the integral of 15(3x-7)^{3/2} ?
The integral of 15(3x-7)^{3/2} is 2(3x-7)^{5/2}+C