What is the integral from 0 to x of x^2+2/(y^2) ?

The integral from 0 to x of x^2+2/(y^2) is diverges

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integral from 0 to x of x^2+2/(y^2)

\int_{0}^{x} x^{2} + \frac{2}{y ^{2}} d y

diverges

Solution steps

\int_{0}^{x} x^{2} + \frac{2}{y ^{2}} d y

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}^{x} \frac{2}{y ^{2}} d y + \int_{0}^{x} x^{2} d y

\int_{0}^{x} \frac{2}{y ^{2}} d y =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

What is the integral from 0 to x of x^2+2/(y^2) ?
The integral from 0 to x of x^2+2/(y^2) is diverges