Question

For the following integral, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition.
∫(x+5)/x^3+7x+5 dx

Answer 1

Answer:

hello your question is incomplete attached below is the complete question

answer :

for  I1 =     $\frac{1}{x^2} + \frac{4}{x^3}$    The integral converges

for  I2 =    $\frac{2x + 6}{2(x^2 + 6x + 4 )}$  The integral diverges

for  I3 =  $\frac{1}{x^2}$  The integral converges

for  I4 = 1  The integral diverges

Step-by-step explanation:

The similar integrands and the prediction ( conclusion )

for  I1 =     $\frac{1}{x^2} + \frac{4}{x^3}$    The integral converges

for  I2 =    $\frac{2x + 6}{2(x^2 + 6x + 4 )}$  The integral diverges

for  I3 =  $\frac{1}{x^2}$  The integral converges

for  I4 = 1  The integral diverges

attached below is a detailed solution