Can you help with these questions please thank you

\fEvaluate 13 dac V9+2 2 Answer:Consider the following indefinite integral. 6x 3 + 2x2 - 47x - 9 dac 2 - 9 The integrand decomposes into the form: C ax + 6+ C - 3 x +3 Compute the coefficients: 0 = C = d = Now integrate term by term to evaluate the integral. Answer: + C\fThe form of the partial fraction decomposition of a rational function is given below. 3x2 + 10x + 4 A Ba + C + ( 20 + 5) (202 + 4 ) C+5 2+ 4 A = B =OC=0 Now evaluate the indefinite integral. 3x2 + 10x + 4 da (z + 5) (202 + 4)For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral. a. (32 2 - 3)3/2 dac a = b . da V5x2 + 6 a = C . *V x2 - 28x + 20 da c = d. da -15 - 5x2 + 20xEvaluate the integral 10m f am 2:4 + 4:132 + 3 Note: Use an uppercase "C" for the constant of integration. C] Make a substitution to express the integrand as a rational function and then evaluate the integral / 3 605(3) dzr: sin2(:c) + sin(:c) Note: Use an uppercase "C" for the constant of integration. [3 Evaluate the indefinite integral. -3 2 + 4x + 4 Answer: + CFor each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral. a. (3x2 - 3) 3/2 due a = b. da V5x2 + 6 C = C . av 7x2 - 28x + 20 da d. da V-15 - 5x2 + 20x a =Evaluate the integral 8 [(33+2$+2)2 da: Note: Use an uppercase "C" for the constant of integration. C] Write out the form of the partial fraction decomposition of the function appearing in the integral: 6:x: 71 f as 2:3 l 5m 6 Determine the numerical values of the coefficients, A and B, where A S B and 6m 71 _ A + B :32 + 52: 6 _ denominator denominator- Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. 14 Consider the definite integral 3 14m :52 do 7 Then the most appropriate substitution to simplify this integral is a: = g(t) where 9(t) = C] Note: We are using t as variable for angles instead of 0, since there is no standard way to type 6 on a computer keyboard. 6 After making this substitution and simplifying (using trig identities)r we obtain the integral / t) (it where a f(t) = [j a : b : After evaluating this integral we obtain: 14 / my 14mmzdmza 7 Make a substitution to express the integrand as a rational function and then evaluate the integral da: :m/ahlel Note: Use an uppercase "C" for the constant of integration. D Evaluate the integral 9:v3 d fw3+ 1 a: Note: Use an uppercase "C" for the constant of integration. C] Evaluate the integral V2/2 3x2 da V1 - 42