What is the integral from 0 to 1 of (2x^2-5)/x ?

The integral from 0 to 1 of (2x^2-5)/x is diverges

Popular >

integral from 0 to 1 of (2x^2-5)/x

\int_{0}^{1} \frac{2 x ^{2} - 5}{x} d x

diverges

Solution steps

\int_{0}^{1} \frac{2 x ^{2} - 5}{x} d x

Expand

\frac{2 x ^{2} - 5}{x} : 2 x - \frac{5}{x}

= \int_{0}^{1} 2 x - \frac{5}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} 2 x d x - \int_{0}^{1} \frac{5}{x} d x

\int_{0}^{1} 2 x d x = 1

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{- \infty}^{0} e^{2 x + 1} d x

\int_{1}^{3} \frac{cos ( x )}{x} d x

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

\int_{1}^{3} (- x^{3} + 6 x^{2} + 7 x - 5) d x

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

What is the integral from 0 to 1 of (2x^2-5)/x ?
The integral from 0 to 1 of (2x^2-5)/x is diverges