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 if n = -1

Q: Find the antiderivative of 5sin x In5 cos x dx 5coS x + C 5sin x In 5 + C O sin x + C In 5 5sin x +…

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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: Find the antiderivative of xe2x/(1+2x)2 from 0 to 1/2

A: Given the integral ∫012xe2x1+2x2dx

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

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Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: 15x²x³43x - 19 The integral f S can be rewritten as (x + 1)²(x² - 6x + 13) Ax + B C D Slax + + ax² +…

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Q: 73. Use the definition of |x\, the chain rule, and the fact that (In x) = - for x > 0 to prove that…

A: Given, dlnxdx=1x, x>0 from definition of x x=x ,     x>0 -x ,  x<0  if x>0 then d…

Q: 32. Find the integral: dx k² +1 (-1)*2 (k² +1) а. +C 5(-1)*2*k k? +1 k+1 b. +C (-1)*2* '(k +1)(k²…

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Q: In(x²+x)-In x+eln 4 dx In e(x+1)

A: Given integral, ∫lnx2+x-lnx+eln4ln ex+1dx

Q: The result of the integral 4 / (x - 1)(x + 1) is equal to -dx Select one: O none of these. ○ In…

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Q: -2-3 Evaluate the integral o S Jy² 2y dx dy.

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Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: -3 Evaluate the integral ſ² ſ² ſ²₁ xz(y + 1)dxdydz

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Q: (a) Evaluate the integral 9x"e¬X dx for n = 0, 1, 2, and 3. n = 0 9. o((-") - (-1)) n = 1 е | n = 2…

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Q: Prove that Jn (x) X good dx=1. n

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Q: 2x² +10x+9 dx = ? x.(x+3) integralinin eşiti aşağıdakilerden hangisidir? X B) In x+3 A) In(x² +3x)…

A: Consider F(x) = 2x2+10x+9x(x+3)2 We will solve it by partial fraction Let Ax+3+B(x+3)2+Cx =…

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…

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Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: What is the antiderivative of 1 / (x - (1/k)x^2) with respect to x? k is a constant

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

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

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Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

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Q: 10. Find the integral of dx x²-4 O In() + C x-2 O In() + C 2x x+2 O fIn( *2) + C X+2 O In() + C x+2…

A: *using concept:- 1. Partial fraction. 2. int(dx/x) = ln(x). 3. ln(m) - ln(n) = ln(m/n).

Q: хах 11. The integral f 4-х2 is equal to 1 A. In | | + C C.-글m14- x리 + C 4 x+2 2+x B. In |4 – x2|+C…

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Q: 7. Evaluate the following integrals. 5x* (a) S ++ sec²x)dx 5x2 (b) S xv7x2 + 12 dx (x + 5) (c) S dx…

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Q: 15x²x³43x - 19 can be rewritten as (x + 1)²(x² - 6x +13) Ax + B C D Slax ² + + lax² + bx+c (mx + n)t…

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Q: 5x Q5 integral Evaluate the in dx (x²+1)(2.x-2)

A: Let I=⇃5xx2+12x-2.dx    I=⇃52xx2+1x-1.dxBy Method of partial fractions…

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: 5x dx. - 6 Compute the integral x2

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Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

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Q: | 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1…

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Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: dx Evaluate the integral: (+3x-7) A ++ In|3x-6|+C 5 +5x+! In/x-21 +C B 3 с +5x+31n|x-2|+C D x² + 5x…

A: You must have idea about logarithmic properties to simplify this expression. Understanding of…

Q: The general solution for D. E. e'y' – + e' = 0 is - x² +xy O y = e¬* + In ( Inlx|+c x+y-1 O y = -x +…

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Q: In x)2 To evaluate aX, apply integration by parts twice. For the second application of integration…

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Q: (1) xyy' + y² = 2x O separable exact O linear in x O linear in y O homogeneous Bernoulli in x…

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Q: 3. Find the integral * dx a² -2 x+1 a.-x - - x - In(x + 1) + C 2 b.x2 – x – In(x + 1) + C c.x2 – x +…

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Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

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

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Q: Find the antiderivative of |5sin x In5 cos x dx · O 5cos x + C O 5sin x + C O 5sin x In 5 + C O 5sin…

A: To find the antiderivative of:∫ 5sinxln5cosxdx

Q: 4 In |x=3| The improper integral dx can be written as: x-3 Select one: 3 In(3-x) dx 4 In(x-3) dx a.…

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Q: 8. The value of the integral 2[x] 1o sulsV ar 3x-[x] dx, where [] denotes the greatest integer 2[x]…

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Q: -X +7 Evaluate the integral: dx (x-2)(x+3) In x - 2|+2 1n x +3 +C 2 In |x – 2| – 2 In |x + 3|+C 2…

A: First of all we will do partial fraction, then we will evaluate the integral.

Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: S √x²-a² X dx

A: To solve the given integral.

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

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Q: A Evaluate the following integrals. 1. S2 dx 2. S6x dx 3. f9° dt 4. S-15x dx 5. S(3x - 4) dx 6. S(7u…

A: As per guidelines, I can answer maximum three subparts of a question. Since you have asked for 11…

Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.