Use the integral test to determine whether the series is convergent or divergent. [infinity] n = 2 n2 n3 + 1 Evaluate the following integral. [infinity] 2 x2 x3 + 1 dx

I think the given series is

You can use the integral test because the summand is clearly positive and decreasing. Then

Substitute u = x ³ + 1 and du = 3x ² dx, so the integral becomes

As u approaches infinity, we have ln(u) also approaching infinity (whereas 1/3 ln(9) is finite), so the integral and hence the sum diverges.

u what ?

step-by-step explanation: