What is the integral of (15)/(2sqrt(x-4)) ?

The integral of (15)/(2sqrt(x-4)) is 15sqrt(x-4)+C

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integral of (15)/(2sqrt(x-4))

\int \frac{15}{2 x - 4} d x

15 x - 4 + C

Solution steps

\int \frac{15}{2 x - 4} d x

Take the constant out:

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

= \frac{15}{2} \cdot \int \frac{1}{x - 4} d x

Apply u-substitution

: \int 2 d u

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

Integral of a constant:

\int a d x = a x

= \frac{15}{2} \cdot 2 u

Substitute back

u = x - 4

= \frac{15}{2} \cdot 2 x - 4

Simplify

\frac{15}{2} \cdot 2 x - 4 : 15 x - 4

= 15 x - 4

Add a constant to the solution

= 15 x - 4 + C

\int \frac{5 x ^{2} + 2 x + 2}{x ^{3} - 1} d x

x \to \infty lim (- x e^{- x})

y^{^{''}} + 2 y^{^{'}} + y = x^{2}, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - y = 0, y (0) = 3, y^{^{'}} (0) = - 1

\frac{\partial}{\partial θ} (r (θ) θ)

What is the integral of (15)/(2sqrt(x-4)) ?
The integral of (15)/(2sqrt(x-4)) is 15sqrt(x-4)+C