# SOLUTIONS TO U-SUBSTITUTION

Jun 21st, 2015
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SOLUTIONS TO U-SUBSTITUTION SOLUTION 10 : Integrate . First rewrite the function by multiplying by , getting (In the denominator use trig identity A from the beginning of this section.) (Use antiderivative rule 5 and trig identity F from the beginning of this section.) truein . SOLUTION 11 : Integrate . First square the function, getting truein (Use trig identity G from the beginning of this section.) . Now use u-substitution. Let so that , or . Substitute into the original problem, replacing all forms of , getting (Use antiderivative rule 4 on the first integral. Use antiderivative rule 6 on the second integral.) (Combine constant with since is an arbitrary constant.) . SOLUTION 12 : Integrate . Use u-substitution. Let so that . Substitute into the original problem, replacing all forms of , getting . SOLUTION 13 : Integrate . First rewrite the function (Recall that .), getting (Now use trig identity F from the beginning of this section.) . On the first integral use u-substitution. Rewrite the second integral and use trig identity F again. Let so that . Substitute into the original problem, replacing all forms of , getting . Use u-substitution on the first integral. Use antiderivative rule 7 on the second integral. Let so that . Substitute into the original problem, replacing all forms of , getting . SOLUTION 14 : Integrate . Use u-substitution. Let so that , or . Substitute into th

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