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Math · Advanced Math
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2. We learned in class how to integrate any rational function using partial fractions. We also noted that any integrand which can be converted to a rational function is then also integrable. Here we will introduce the Weierstrauss substitution, t tan that converts some trigonometric integrals to rational functio a) By writing cosas show that sec cos- V1+t2 1 + t2 and also that 2t sin .12 1 + t2 Hint: Consider the quantities cos 20 and sin 20 (b) We will now employ the results of part (a) to integrate J-1/V2 .. Using the trigonornetric substitution x = sinu, show that T/4 1 + cos 2uli. Now write v 2u and then apply the Weierstratuss substitution results from part (a) to yield an integrand that can be integrated using the method of partial fractions. Consequently, show that 1/v2 2arctan-

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