This is the same question as Example 3 in the Integration by Parts section in IntMath. We need to alternate the signs (3rd column), so our 4th row will have a positive sign. Using the Tanzalin Method requires 4 rows in the table this time, since there is one more derivative to find in this case.
We then multiplied (1) by (−sin x) and changed the sign.Īdding the final column gives us the answer: We multiplied ( x) by (−cos x) and we didn't change the sign. We'll go straight to the Tanzalin Method. We can then factor and simplify this to give: (We add the constant of integration, C only at the end, not in the table.) The answer for the integral is just the sum of the 2 terms in the final column. We assign a negative sign to the product, as shown. We then multiply the 2 terms with yellow background (the first derivative and the second integral term). We just multiply the 2 terms with green background in the table (the original 2 x term and the first integral term). In the second column are the integrals of the second term of the integral. (We need to choose this term for the derivatives column because it will disappear after a few steps.) In the first column are successive derivatives of the simplest polynomial term of our integral. In the Tanzalin Method, we set up a table as follows.
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