Please solve, I believe part (a) converges because of the p test p>1 but using the comparison test is tricky because (1+sinx)/x^3 is not greater than 1/x^3 for every case of x. So how do you explain it? For part (b) I'm getting a value of 21 and is convergent.

a. Is the following improper integral convergent. Explain your answer. 1 + sin x 23 dx b. Is the following improper integral convergent. If so evaluate it. .8 1 2 2 / 3 dac