Consider the indefinite integral / 7x+ 6x-+ 5x + 3 x4 + 1x2 Then the integrand has partial fractions decomposition a b CI + d + - + x2 +1 where b= d= Integrating term by term, we obtain that 7x' + 6x- + 5x + 3 de = to Question Help: DVideo Submit QuestionConsider the indefinite integral /- 6x + 5x- - 18x - 20 dx x2 - 4 Then the integrand decomposes into the form C d ax + b+ x- 2 C+2 where b = Integrating term by term, we obtain that 6x + 5x- - 18x - 20 di = 12 - 4 Question Help: D Video Submit Question\f1222 dzr V36 o {A) Which trig substitution is correct for this integral? O x = 36sin(f) Oz = Gsec(f) O x = 6sin(f) O x = 6tan(d) Oz = 36 tan(d) O x = 36sec(d) Evaluate the integral: f {B) Which integral do you obtain after substituting for = and simplifying? Note: to enter 8, type the word theta. Tl P {C) What is the value of the above integral in terms of &7 . (D) What is the value of the original integral in terms of x? L Question Help: [E] Video Submit Question Evaluate the integral: /' V25 2 - " dr 2z (A) Which trig substitution is correct for this integral? O x = 25sec(f) O x = 25sin(8) O x = 5sec(#) O x = Hsin(d) O x = 25tan(f) O x = 5tan(f) (B) Which integral do you obtain after substituting for = and simplifying? Mote: to enter 8, type the word theta. [ {C) What is the value of the above integral in terms of &7 | e (D) What is the value of the original integral in terms of z? e Question Help: [] Video Submit Question 14 x24/x? + 36 e {A) Which trig substitution is correct for this integral? Oz = 36sin(f) Oz = 14dsec(f) Oz = 36sec(f) Oz = 6Gtan(d) Oz = 6Gsin(f) Oz = 36tan(f) Evaluate the integral: f {B) Which integral do you obtain after substituting for x and simplifying? Note: to enter f, type the word theta. [, {C) What is the value of the above integral in terms of 67 . C (D) What is the value of the original integral in terms of x? +C Question Help: [E] Video Submit Question 23v x2 - 25 Evaluate the integral: (A) Which trig substitution is correct for this integral? Or = 23 sin(0) Or = 5tan(0) Or = 5 sin(0) Or = 25 tan(0) Or = 5sec(0) Or = 25 sec(0) (B) Which integral do you obtain after substituting for c and simplifying? Note: to enter d, type the word theta. de (C) What is the value of the above integral in terms of e? C D) What is the value of the original integral in terms of a? + C Question Help: DVideo Submit QuestionEvaluate the integral: f v 64x? 49 dz T {A) Which trig substitution is correct for this integral? Ox= sec('] Oz= gsec('j Oz = %sec{i?} Oz = gsec{l?} Or= %sin{] (B) Which integral do you obtain after substituting for =7 Note: to enter 8, type the word theta. f df {C) What is the value of the above integral in terms of 67 (D) What is the value of the original integral in terms of z? Note: WAMAP does not recognize the inverse secant (arcsec) function. You will need to use another inverse trig function when you fill in your answer below. +C Question Help: [ Video (1) Evaluate / cos xdx Hint: Express cos* x in terms of sin c. Then use the substitution u = sin . Back substitute to write your soluton in terms of x solution = + C (2) Evaluate / cos xdx Hint: Use the half-angle identity cos* * =- (1 + cos 2x) solution = + C Question Help: Video 1 Video 2 Submit Question\f