Determine-whether-the-improper-integral-converges-or-diverges-1-2x-7-7x-3-5x-2-1-dx-

Question Number 140823 by liberty last updated on 13/May/21

Determine whether the improper

integral converges or diverges

\int_{1}^{\infty} \frac{2 x + 7}{{7 x}^{3} + {5 x}^{2} + 1} dx

Commented by liberty last updated on 13/May/21

can anyone help me

Answered by mathmax by abdo last updated on 13/May/21

x \to \frac{2 x + 7}{{7 x}^{3} + {5 x}^{2} + 1} continue on [1, a [so integrable on [1, a [(a > 1)

at + \infty \frac{2 x + 7}{{7 x}^{3} + {5 x}^{2} + 1} \sim \frac{2}{{7 x}^{2}} and \int_{a}^{\infty} \frac{2}{{7 x}^{2}} dx cv \Rightarrow this integral is cv .