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Using Partial Fractions In Exercises 3-20, use partial fractions to find the indefinite
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Calculus: Early Transcendental Functions (MindTap Course List)
- Integrate using partial fractions only S x+2 x²-3x²+2x -dx Provide your answer below:arrow_forwardUse partial fractions to find the integral. 4- X | 2x² 2x² + x1 Step 1 Rewrite the polynomial as 2x² + x1 = 2x² - x + 2x - 1. Collect the terms according to the power of x on the right side and factorize. 2x² + 2x -x-1 = x(2x − 1) + (2x - 1) = (2x - 1)(x + 1) Because 2x² + x − 1 = (2x − 1)(x + 1), you should include one partial fraction for each factor and write A 4-X 2x²+x-1 where A and B are to be determined. dx To solve for A, let x = 1/2✔ 1 x 2 4 2x Step 2 Multiplying this equation by the least common denominator (2x - 1)(x + 1) yields the basic equation 4x = A(x+1 + B(2x - 1). Step 3 The most convenient values are the ones that make particular factors equal to 0. 7 x+1 Because this equation is to be true for all x, substitute any convenient values for x to obtain equations in A and B. Step 4 To solve for B, let x = 4 1/2 and obtain 4 − —⁄2 = A ( ²¹1 + 1) + B( ² × 1⁄2 − 1) 2 - 2 A = 7/3 X = AX 4 + 1 = A(-1 2x = 4 B = -5/3 1 2 + 5 x 7/3 x X to obtain the following. + 1) + B(2(-1 B X…arrow_forwardx-1 (a) Use partial fraction decomposition to evaluate x² - 2x - 3 (b) What's another method we could use to evaluate this integral? Explain why. You do not need to evaluate the integral again using this other method. da. Show all of your work.arrow_forward
- 6arrow_forwardTutorial Exercise Use partial fractions to find the indefinite integral. 16x²-1² dx Step 1 Rewrite the polynomial in the denominator as 16x¹ - 1 = (4x2)2 - 1² = (4x²-1)(C =((2x)²-1²)(C = (2x - 1)(2x + 1) (1 x²+1). youarrow_forwardEnvironmental Science The predicted cost C (in thousands of dollars) for a company to remove p of a chemical from its waste water is given by the model C=120p10000p2,0p100. Write the partial fraction decomposition for the rational function. Verify your result by using a graphing utility to create a table comparing the original function with the partial fractions.arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage