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- Please circle and write in clear lines when showing the steps for the final answer in case I understand. I appreciate you. Thank youarrow_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_forwardIntegrate by partial fractions the followingarrow_forward
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