In(x²+x)-In x+eln 4 dx In e(x+1)

Q: Express z = 12 (cos 225° + isin 225°) into its exponential form. ww

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Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: 6. Evaluate the integral ex e* +e-xdx

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Q: 1-In (-) + In(2x³) = In3 2- 4 log 2 – log3 + log16 = x 3-Expand In [x? sin3 x /Vx2 +1]

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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: 1. Integrate: e3x cos(x) dx

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Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: Evaluate In x dx x3 А. In x x3 1 In x 2x2 1 + C 4x2 В. In x dx 1 1 x3 In x - 2x2 4x2 + C С. In x dx…

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Q: Solve the integral. 6х — 3 1.5 -dx 4x2 – 4x + 1

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Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

Q: In x Evaluate S 2 x(4-ln² x) O2 ln | 4 - In² x | +C Oln | 4 - ln² x | +C O ln | 4 - In² x | +C Onx…

A: Given ∫lnxx4-ln2xdx

Q: %3D In( cosh(9x) + sinh(9x)) + In( cosh(9x)- sinh(9x)) = Select one: O None 0 9 O zero O9 cosh(9 x)…

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Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

A: Given: lncosh(11x-sinh(11x)) We know that   cosh(x)=ex+e-x2        sinh(x)=ex-e-x2   Then…

Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

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Q: 2(1-z) Evaluate S S --) dy dx dz

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 16 |how do you express limn→0 0 Li=1 - (5+ £)9/ as п definite integral

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: 5. Find the integral 1 -dx x -5x +6

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Q: .2 -dædy In (x) ey

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Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: 1. Integral e-9x dx

A: We have to solve above integral

Q: In x – In c – 2 1 +- sin 2 - = 0 - 4x In-- 2y +x sin- 2y = 0 X -

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Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

A:

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: 2 16n |xV8 - x³ dx: 9/3 3 11) Show that

A: Properties of Beta Function:  β(m, n)=∫01xm-11-xn-1dxβ(m, n)=Γ(m)Γ(n)Γ(m+n) ;       m>0,  n>0…

Q: 5 Only one of these calculations is correct to evaluate the definite integral 7x In(x) dx Using the…

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Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: 3. Find the integral x² +12x +12 dx x' - 4x

A: Given,            ∫x2+12x+12x3-4xdx

Q: 5. Express the integral: e- dr in terms of gamma function.

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Q: If x >0, Prove that X - ln (1+x ) > x^2/2+2x

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Q: 6. Evaluate the integral. x³e2x dx

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Q: 1261 (2x+1 dz 4-3x -x² 1 (((x+) dx (3) 28 (2x-3 dx √(x²-1) (2x+3) 31 32 33 dx √(x²+1) (2x+1) alx…

A: Note: As per Bartleby guidelines only the first question has been solved. Given: The function is…

Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow…

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Q: Г(x3 + 2х — 1) cos 4x dx A .3 13 x (3x² 13 sin 4x + 4 |cos 4x + C + - 4 32 16 128 B (x³ (3x² 13 |cos…

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Q: 6. Evaluate the integral dx (4x2 + 1)(x² + 4)

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Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: how do I find the integral of e^-xsec^2(e^-x)dx

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Q: 19. f(x. y) In(1 - x - y) %3D

A: As per our company guidelines we are supposed to answer only the first question that you have…

Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

A:

Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

Q: 5.f(x) = x (x - 1)(*- 2)(* + 1) As x + +o, f(x) = As x - -n, /(x) As x > I co, f(x) – As x > w./(x)…

A: Solution is given below:

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

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Q: - In-2. Hence show that In = 01 tan" x dx = n - 1

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Q: 1. Evaluate the integrals that converge: dx 2x ! dx (x2 + 5)3 b) a) 3-x - 00

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Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: 2x²-3x + 10 dx (x²+4)2

A: The objective of the question is evaluate the indefinite integral.