What is the integral of (sqrt(4-9x))/x ?

The integral of (sqrt(4-9x))/x is 2sqrt(4-9x)-2ln| 1/2 sqrt(-9x+4)+1|+2ln| 1/2 sqrt(-9x+4)-1|+C

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integral of (sqrt(4-9x))/x

\int \frac{4 - 9 x}{x} d x

2 4 - 9 x - 2 ln \frac{1}{2} - 9 x + 4 + 1 + 2 ln \frac{1}{2} - 9 x + 4 - 1 + C

Solution steps

\int \frac{4 - 9 x}{x} d x

Apply Integration By Parts

: 4 - 9 x - \int \frac{9 x - 8}{2 x - 9 x + 4} d x

= 4 - 9 x - \int \frac{9 x - 8}{2 x - 9 x + 4} d x

\int \frac{9 x - 8}{2 x - 9 x + 4} d x = - - 9 x + 4 + 2 (ln \frac{1}{2} - 9 x + 4 + 1 - ln \frac{1}{2} - 9 x + 4 - 1)

= 4 - 9 x - (- - 9 x + 4 + 2 (ln \frac{1}{2} - 9 x + 4 + 1 - ln \frac{1}{2} - 9 x + 4 - 1))

Simplify

4 - 9 x - (- - 9 x + 4 + 2 (ln \frac{1}{2} - 9 x + 4 + 1 - ln \frac{1}{2} - 9 x + 4 - 1)) : 2 4 - 9 x - 2 ln \frac{1}{2} - 9 x + 4 + 1 + 2 ln \frac{1}{2} - 9 x + 4 - 1

= 2 4 - 9 x - 2 ln \frac{1}{2} - 9 x + 4 + 1 + 2 ln \frac{1}{2} - 9 x + 4 - 1

Add a constant to the solution

= 2 4 - 9 x - 2 ln \frac{1}{2} - 9 x + 4 + 1 + 2 ln \frac{1}{2} - 9 x + 4 - 1 + C

y = \frac{x ^{2}}{1 + x}

x \to 0 lim (\frac{2 x}{x ^{2} + 1})

\int (\frac{sin ( x )}{x}) d x

\frac{\partial}{\partial x} (2 x - 3 yz)

What is the integral of (sqrt(4-9x))/x ?
The integral of (sqrt(4-9x))/x is 2sqrt(4-9x)-2ln| 1/2 sqrt(-9x+4)+1|+2ln| 1/2 sqrt(-9x+4)-1|+C