What is the integral from 0 to 1 of 1/(2-3x) ?

The integral from 0 to 1 of 1/(2-3x) is diverges

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integral from 0 to 1 of 1/(2-3x)

\int_{0}^{1} \frac{1}{2 - 3 x} d x

diverges

Solution steps

\int_{0}^{1} \frac{1}{2 - 3 x} d x

Find undefined (singularity) points:

x = \frac{2}{3}

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

\int_{0}^{\frac{2}{3}} \frac{1}{2 - 3 x} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\frac{d y}{d x} + 3 x y^{3} = 0

\int \frac{5 t - 4}{t + 1} d t

x \to - 1 lim (0)

\int (1 - x)^{- 3} d x

\int x^{3} 1 - x^{4} d x

What is the integral from 0 to 1 of 1/(2-3x) ?
The integral from 0 to 1 of 1/(2-3x) is diverges