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Unformatted text preview: expressing tangent in terms of sine and cosine. Now you can use u-substitution to solve the integral. A lot of mathematicians do not like negative signs in the answers to their integrals. Notice that by using a log property you can move the negative into the exponent. Then you can replace the cosine term with a secant. A similar method can be used to find the integral of cotangent. Expressing secant in terms of cosine doesnt leave a term for the du in a u-substitution. Instead, try multiplying secant by some expression equal to one. This integral might look more complicated, but it can be evaluated by u-substitution. The numerator is exactly the derivative of the denominator. Dont forget to express your final answer in terms of x and not u . Notice that evaluating trig integrals involves knowing a few tricks. The more of these tricks you see, the more integrals you can solve....
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- Spring '10