1 Consider the integral #(x+1)²(x² + 1)² dx. Without evaluating the integral, rewrite the ntegrand as a sum of simpler fractions. You do not need to find the unknown coefficients. Simply state he simpler form of the integrand.

Q: 1) Solve the following integral 1 dx. xV4x4 – 1 - ii) Determine whether the following integrals…

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Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b

Q: Q5. Find the below integrals and √(2.20) 2717 dx(x) = 2₁ (0,00) 1 + X{0,3} + X(-3,-2)) "dX=? where A…

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Q: (2) Evaluate the definite Integral √² (6x +9) dx

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Q: Solve the integral: A B с 1 √√x+x √√ Sin/1+x²|+c -In +C 6in|5+ x²|+C с {in/1+x³ |+c C dx

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Q: The value of the improper integral 42 x² e¯¤* dx 1 - 14e 14e-1 - O 14e-1 O 42e-1 O – 42e-1

A: Explanation of the solution is given below...

Q: 4 5y²-8X+6) dx =?

A: To evaluate the given definite integral

Q: The definite integral is equal to O 2 [²x Select one: 4 O f₁²₁x² dx + ₁ + x² dx none of the others ○…

A: ∫02 x2dx here we have to find equal to this. split the integral into two  use formula  ∫a  b f(x)dx…

Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: 3. Evaluate the integral. (a) -2/3 dx

A: Evaluate the integral

Q: 1. Evaluate the integrals x³e- dx

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Q: Evaluate the integral. √3 5 1/√31+x² dx

A: NOTE: Refresh your page if you can't see any equations. .

Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: 1. Evaluate the integral of x2 (3 - 2x) dx if upper limit = 2 and lower limit = -1. а. 12 b. -12 C.…

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Q: To treat the integral -44(2x + 1)-2 dx as a constant multiple of one of the form u'u' dx, we let n =…

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Q: Evaluate the integral 4 + 4) (x² + 4x + 2)*dx by making the substitution u = x2 + 4x + 2. + C NOTE:…

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Q: Solve the Indefinite Integral. xe²t S dx (2x+1)² A [1-21] +0 e2x 2x C 4 2x+1 B. 2-2(22+1) + C 4 C.…

A: SOLUTION-

Q: Evaluate the integral. dx (х — 9)(х — 18) (Use symbolic notation and fractions where needed. Use C…

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Q: 11. The integral of an(In|4x=12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. С. 4 D. I

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Q: 1) Find the integrals: i) i) SF Inx dx 4-X2

A: Part i          ∫x2-14-x2dx

Q: What must be the value of C (constant of x² - 4 -dx so that the x +2 integration) to the integral of…

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Q: Consider the following indefinite integral. 6x3 + 5x² – 47x – 36 dx x2 9. The integrand decomposes…

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Q: The integral of sin2 3xdx is x 1 -x +A + C, What is the value of A if x =-. 4 O -1/12 O 1/12 O 1/18…

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Q: Evaluate the integral. -1/4 S" 5 sin* 2nx dx

A: here we us the sine reduction formula to solve the given problem ∫(sinnx) dx=-cos(x)(sin…

Q: Evaluate the integral. dx (х — 13)(х — 23) (Use symbolic notation and fractions where needed. Use C…

A: Explained below

Q: 1) Consider the indefinite integral  ∫ X5/(x6-4)6 dx  This can be transformed into a basic…

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Q: 2) Consider the integral (3x+ + 8) dx a) Rewrite the integral as a Right Riemann Sum with n = 4…

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Q: 9/ Approximate the follwoing integrals using The Simpson's ruls @ 0-25 b (Cosx) dx -0-25 Š 0-5…

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Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

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Q: d) Determine the infinite integrals of the following e+2 i. ii. 2 3 sin2x dx

A: Evaluation of the integral

Q: d) Determine the infinite integrals of the following i. ii. JF 3 sin2x dx

A: Evaluate the definite Integral

Q: 72. (a) Use integration by parts to show that, for any positive integer n, dx (x² + a²)" dx 2a (n -…

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Q: Evaluate the indefinite integral. S(4v – v²)² dv , and Show the complete solution and express the…

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Q: 2. 36 +x² dx =)

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Q: 11. The integral of tan(In|4x²|) dx is bln|sec(ln(2x)ª)|. What is b? А. 2 В. 1 D. ! С.4 4

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Q: 11. The integral of an(In|4x-12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. 2 С. 4 D.

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Q: Evaluating the integral (cos x- 2sin x)dx gives: А. -2 В.О С. 1 D. -4

A: Option D is correct Explanation is given below

Q: Evaluate the integrals ∫(2θ + 1 + 2 cos (2θ + 1)) dθ

A: To evaluate ∫2θ+1+2cos2θ+1dθ

Q: 3. (а) Evaluate the indefinite integral 2Varctan(3x) dx. 1+ 9x² •16 (Б) Suppose we know that (3f (x)…

A: (a) We need to evaluate the following integral ∫2arctan(3x)1+9x2dx (b) We need to evaluate the value…

Q: 1 (x² +a) b dx is In 5x The resulting integral of +eTan-1 + C, where a, b, d, and e are integers. x³…

A: Given:∫5xx3+x2+4x+4dx= ln⁡x2+a1bx+d+eTan−1⁡x2+C Let, I=∫5xx3+x2+4x+4dx ⇒I=∫5xx2(x+1)+4(x+1)dx…

Q: Evaluate the integral. dx (х — 4)(х — 8) (Use symbolic notation and fractions where needed. Use C…

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Q: (a) Solve the following integrals. (i) (ii) x' + 3x? – 10 - dx x(x – 3)(x+1) Integrate er* cos (3x)…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3 Given that / et dx = e3 - e, use the properties of integrals and this result to evaluate (4ex - 5)…

A: To find the integral by using the given results.

Q: Consider the indefinite integral Ва3 + 21? + 5а + 0 dx x² – 1 | Then the integrand decomposes into…

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Q: Evaluate the given definite integral. -2 . Jx(3-x²)*dx -3 -2 S2x(3-x)°d dx = (Type an integer or a…

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Q: 1. Evaluate the integral. -1 (6х — 12) dx

A: To evaluate the given integral.∫3-16x-12 dx

Q: In the indefinite integral J 3x²e* dx, the integrand is A 3r © 3x2 D x³+C B.

A: The given integral,    ∫3x2ex3dx

Q: 5. Calculate the integral f sin"( 1) cos'( t) dt, Your solution will be an expression in terms of m.…

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Q: Find the indefinite integral. -6w ſe " sin2w dw 3sin2w+cos2w-ów 20 sin2w- 3cos2w +C 20 -sin2w-…

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