Question: Please show all the steps in your solutions to the following problems. Problem 1 Evaluate the following indefinite integrals: 1. Stan(x) dx. 2. fx cos(r)

Please show all the steps in your solutions to the following problems. Problem 1 Evaluate the following indefinite integrals: 1. Stan(x) dx. 2. fx cos(r) 3 sin(x) dx. Problem 2 Evaluate the following indefinite integrals: 23 1. 5 x2 - 1" =dx. 2. fin(x)rVx2 - Idx. Problem 3 Evaluate the following indefinite integrals: 2 1. J 72 -25 -dx. x3 - 2x2+ 2-1 2. J 73 - 422 +5x-2" H 3. (Bonus) J 4 + 2x2 + 1dI. Problem 4 Determine whether the following improper integrals converge or diverge (you do not need to compute the value of the integral in case of conver- gence): 1. Se x In(x) 2 dx. e - I 2. Ji + In(x) dx. 1 + 3sin*(6x ) x. 3. J1 71/3 ( 2 - e-20 ) Problem 5 Evaluate the following improper integrals in case they converge: 1. Jo 12 + 2 + 2 -dx. 2. SP -edx

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