Question: 7. Integrate using the substitution rule a. S cos' x (sin(x)) dx b. S 6x2(4x3 + 9)' dx c. Soxv9 - x2 dx 8. A

7. Integrate using the substitution rule a. S cos' x (sin(x))

7. Integrate using the substitution rule a. S cos' x (sin(x)) dx b. S 6x2(4x3 + 9)' dx c. Soxv9 - x2 dx 8. A student was asked to evaluate the following integral So x4(x5 + 1)5 dx Their work is shown below. Did they solve this correctly? If they made a mistake, explain the mistake and show the correct work from that point on. * 4 ( x 5 + 1 ) olx let u = x 3 + 1 x* ( u ) du du - 5 x4 5 x4 dx dx = dy 5 x 4 J su du F ( x ) = $ ( 6 ) u " F ( x ) = u = 1 (2 ) - 1 (-1 ) ' 30 30 65 13 30 30 30 6

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