What is the integral from 0 to 1 of 1/(5x-3) ?

The integral from 0 to 1 of 1/(5x-3) is diverges

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integral from 0 to 1 of 1/(5x-3)

\int_{0}^{1} \frac{1}{5 x - 3} d x

diverges

Solution steps

\int_{0}^{1} \frac{1}{5 x - 3} d x

Find undefined (singularity) points:

x = \frac{3}{5}

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

\int_{0}^{\frac{3}{5}} \frac{1}{5 x - 3} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

2 y^{^{''}} + y^{^{'}} - y = x + 1

x \to 3 lim (x^{2} + 4 x - 3)

\frac{d}{d x} (x^{3} - 4)

\int (1 - x)^{5} (x + 1)^{2} d x

f (x) = x^{2} + 3

What is the integral from 0 to 1 of 1/(5x-3) ?
The integral from 0 to 1 of 1/(5x-3) is diverges