What is the integral from 0 to 2 of (5x-15)/(2x-3) ?

The integral from 0 to 2 of (5x-15)/(2x-3) is diverges

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integral from 0 to 2 of (5x-15)/(2x-3)

\int_{0}^{2} \frac{5 x - 15}{2 x - 3} d x

diverges

Solution steps

\int_{0}^{2} \frac{5 x - 15}{2 x - 3} d x

Find undefined (singularity) points:

x = \frac{3}{2}

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{\frac{3}{2}} \frac{5 x - 15}{2 x - 3} d x + \int_{\frac{3}{2}}^{2} \frac{5 x - 15}{2 x - 3} d x

\int_{0}^{\frac{3}{2}} \frac{5 x - 15}{2 x - 3} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

y = x^{2} arctan (5 x)

x \cdot sin (x)

\frac{d y}{d x} = k x

\int \frac{18 x ^{3} - 36 x ^{2} + 4}{x ^{2} - 2 x} d x

e^{8 x}

What is the integral from 0 to 2 of (5x-15)/(2x-3) ?
The integral from 0 to 2 of (5x-15)/(2x-3) is diverges