5) For each of the integrals, find the needed rationalizing substitution to obtain an integral that...
(1 point) Calculate the integral below by partial fractions and by using the indicated substitution. Be sure that you can show how the results you obtain are the same. 1. 2x - dx 1 x² – 64 +C. First, rewrite this with partial fractions: I ZX64 dx = | dx + dx = (Note that you should not include the +C in your entered answer, as it has been provided at the end of the expression.) Next, use the substitution...
please help 11. Use a Table of Integrals and an appropriate substitution to find: 34 +9e? +7e" dr Vez -36 Math&152 - Calculus II Name: -100% +50x² - 66x +36 -dx 5. Integrate: 25x² +16 Hint: Notice that the Degree(Numerator) > Degree(Denominator). So we will do the long division 14 and then do partial fraction decomposition on the remainder if necessary. x2 +11 4. Evaluate S dx by the partial fraction decomposition (x-3)(x2+4)
(1 point) For each of the following integrals, select an integration technique that could be used to evaluate the integral. The same answer may occur more than once. x-4 dx 2x2 + 3x - 2 1 dx (4 - x2) sinh*(2x) dx l [ sinh | 28#3x-2 2x2 + 3x - 2 dx x2 - 4 Use a substitution u = 2x^2 Use a substitution x = 2sin(t) Use hyperbolic double angle formulae Use hyperbolic identities and a substitution u...
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
*PROBLEM 1 Using Two Methods Find the indefinite integral (a) using a table of integrals and (b) using the given method Integral Method 3 Integration by parts In dx *PROBLEM 1 Using Two Methods Find the indefinite integral (a) using a table of integrals and (b) using the given method Integral Method 3 Integration by parts In dx
Test: Final This Question: 6 pts Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. XX Which substitution transforms the given integral into one that can be evaluated directly in terms of 0 OA. X 3 tano OB. X= 3 sino OC. X= 3 sec 0 Given the expression for x above, find dx in terms of O and do. dx = 00 dx x4-9 Click to select your answer(s).
Characterize the below integrals (definite or indefinite) and solve the integrals by using the substitution rule: a. S(-11(5x + 7)5)dx b. S(4V7x - 1)dx C. J-8 siz3x cosx) dx d. S -6 dx 2x+3 e. S(-5sin(9x - 4))dx
Please show all steps. Evaluate the integral using a trigonometric substitution. Jo (4 – x2) 312 * - *2)3/2 dx
Using trigonometric identities and substitution, evaluate the following integrals: 1. S sin5 x dx 2. Shamrzdx 3. S V4 – 9x2dx 4. Sýsin? x dx 5. S 1 dx x2 +81
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)