Find each antiderivative using any method. 33. + 4 dx r[( In x)³ – 4( In x)²+ 5] 34. dx, x > 0 8x + 10 In x + 5 35. dx 36. 5х — 4 (x + 4)² dx 37. dx 38. (3х - 2 x2 39. Evaluate 5* dx without using Table 1. (Hint: 5 = e ln 5.)

Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…

A: Find the anti derivative.

Q: 5. Evaluate the integral 2 c2x x2 (x² + 2y³) dy dx.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: ! 6-Find the value of the integral * U x3/2 e-x dx

A:

Q: 8. Evaluate the integral. 2 2 (a) S(4x°. 3x + 2x)dx - 1 4 4+6u (b) S(ou)du Vu 1

A: Using rules of integration & formulae of integration.

Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

A:

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A: The integration are

Q: Find the most general antiderivative. 9 dx -x2 x zX - IN

A:

Q: 6. Let a be a positive constant. Determine the general antiderivative of a using the fact 1 a² + x2…

A:

Q: 5) Find the general antiderivatives for the following; х-1 dx x* +2х-3 -dx 6)

A:

Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

A:

Q: Find the antiderivative of: xn+1 [(n + 1) In x – 1] if n+ -1 x" In x dx = (n + 1)² 1 (In x)² + C 2…

A:

Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: 1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and…

A: As asked we can answer question no 1 and 4 as below.

Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

A:

Q: 13)Evaluate 13 Evaluate the integral s 5x--Xt27 dx x (x²+G) -1 3 tan 3+C b)(-ト2フx)、1mlxCx?ss)1c Sx3…

A:

Q: Find the most general antiderivative. 2 7 dx X+1

A: By using integration formula, we calculate the given integral.

Q: Find the antiderivative of dx / (25 + 4 x^2) * O (1/2) arctan (x/5) + C O (1/10) arctan (2x/5) + C O…

A: An antiderivative is an integral process that can help a function to get back into its parent…

Q: 2. Use the substitution u = x² and then Integration by Parts to evaluate / x³e**dx.

A: Given: ∫x3ex2 dx We substitute u=x2, that implies du=2x dx. By using this substitution, ∫x3ex2…

Q: Evaluate (indefinite integral) (4x^2.5 - x^e - 2sinx)dx (t^3 + 5t^2 - 4)/ (t^2) dt

A:

Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

A:

Q: 1 Find the most general antiderivative of the function x3 + 4x

A:

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 2+In3 +C (3e)3+cosh2x B) 2+2ln3…

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: 2. Integrate: x² In x dx a. In x+c. b. [(In x)² ++c c. [(Inx)² - Inx+]+c d. none of these

A: The given integral is x2lnx.

Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

A:

Q: 5. Evaluate the integral. 1 -dx æ² – 1 a) b) S. +4 -dx x² + 4

A:

Q: Evaluate the following indefinite integrals. 1. S(5x + 4)11 dx 2. Sx (x² + 2)17 dx 3. fx²(9 – x³)5…

A: The solution is given below

Q: One of the correct. steps to evaluate x²inx. x²Inx dx to yield the correct integral (A dx x2Inx B x³…

A: The given integral,     ∫x2lnx dx

Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

A:

Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

A:

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: Step by step

A:

Q: e2x 2.) S. dx ex – 5

A:

Q: Create a second order DE (no need for IC's) whose sdution conuergio to O ao t+ o, without…

A:

Q: 02:- By using integration by part, find :- (Choose two only) 1- Sxe-* dx 3-S(1+ x²)e¬*dx 2-f Inx…

A: As per the company guideline's we are supposed to answer first question as mentioned by the…

Q: 1. Evaluate the integral 2 dx x2 +4x + 20

A:

Q: 2. Evaluate the integral x(3 – 5x) (3x – 1)(x – 1)2 dx

A: To solve the following integral

Q: One of the correct steps to evaluate x²lnx dx to yield the correct integral (A x2 – 2 | dx x³Inx В…

A:

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+cosh2x A +C 2 + 2ln3 (3e)3+cosh2x 2ln3…

A:

Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+cosh2x B 2ln3…

A:

Q: ormulas to compute the following antiderivative. x-1 x² -dx.

A:

Q: Q1/ Evaluate 1 dx Jo 1+x² using Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: Simpson's rules are techniques of numerical integration. Both 1/3 and 3/8 rules are explained in the…

Q: 15. Evaluate the integral 10 ·dx (x – 1)(x² + 9)

A:

Q: Using Simpson's method Vx dx for n=4 is equal to

A: We have to evaluate ∫01xdx for n=4.

Q: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

A:

Q: Q1\ Evaluate the integrals: 10 A. S- V16+x2 В. Г(3 — 2х)-5 dx

A:

Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu

Q: Find dy/dx by the implicet differentiasion x2+y2=64

A: