Problem 4. Consider the integral x³ x² +9 J (a) According to lectures, which substitution should we try if we see the term √x² + a²? 27 dx. (b) Make a substitution to show that our integral is equal to 7 S (c) Using another substitution, show that Ita tan³0 sec 0 d0 = 9 sec³ 0- 27 sec 0 + c. (d) Suppose we have the following triangle: 27 tan³0 sec Ꮎ dᎾ . 3 NOT TO SCALE X Using SOH CAH TOA, what is the value of tan 0? What is the value of the hypotenuse? What is the value of cos 0? What is the value of sec 0? (e) Evaluate the integral given at the start of the question.

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