54, y = (ln x)cos* cos x %3D

Q: Find cosh 2x sinh? 2x dx.

A:

Q: 2. cos“ y sin’ ydy

A:

Q: 22. Evaluate S tanºx sec² x dx

A:

Q: e sinh 2x dx

A: The given integral,       ∫e-xsinh(2x) dx

Q: 44. y" +y = secr· csc x

A: Consider the equation, Let the homogeneous equation is The standard form of this equation is The…

Q: 17. sech? x tanhx dx 12

A: Integrated by substitutions

Q: (x?1) ore sin2x dx

A: Integrate by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫df(x)dx·[∫g(x) dx] dx +C

Q: 4 x ) dx. 4 tan x

A: topic - definite integral using integration properties

Q: sinh In(2+2x) dx? x+1

A:

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

A:

Q: If f(x) = (52² + lx + 6)cos(x), find f'(x) =

A:

Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Find dx by using logarithmic differentiation for = (Cos x)(e)

A:

Q: Find ∫e^(2x)sin(2x)dx

A: Given: ∫e2xsin(2x)dx

Q: 3 ſ dx – S sin²5xdx

A:

Q: 7. S (x-1+cosx) cos2(sinx+lnx)

A: We use substitution method to solve this integration

Q: 4. f(x) = -sin Зл PS = DCP 11 VS =

A: We have to find the amplitude, phase shift, vertical shift and period of the given function.…

Q: 12, S a cos Vx dx COS

A:

Q: 1. ( sinhx - sinhx +coshx coshx dx

A: We have to find

Q: Find /e2x sin(2x)dx

A:

Q: 2- Solve the equation for x : Cosh x = Sinh x +1/2.

A: We need to find out the value of x. The given equation is Cosh x=Sinh x+12 Now,  Cosh x=ex+e-x2  and…

Q: y = ln° '(n*))) (tanh²(sec

A:

Q: 3+ cos(log, x) xp- x sin?(log, x)

A: Given I=∫3+cos(log4x)x sin2(log4x)dx Let assume log4x=t ⇒1x ln 4dx=dt⇒dxx=ln 4 dt

Q: 2. y = [log(arccotx³)]coshx. Find dy/dx

A:

Q: Calculate the higher derivative. (Use symbolic notation and fractions where needed.) d? 8 cos (1) =…

A: To find,  d2 dt28 cos2(t)

Q: A. Evaluate. 1 (sinhx - sinhx +coshx cosh?x 1. dx

A:

Q: S(sin 29x + 6e0 +5 cos 5x+)dx

A: Given integration ∫sin29x-x5+6e6x+5cos5x+x5dx  Now we break it and we get   ∫sin29xdx-…

Q: fxcos (x)dx COS

A: Assume u=x^2Find du

Q: 8e cos 2x dx csc(x) sec(x)

A:

Q: Find dx 1- y = log (Sin x )- Cot - Vx 3 2. y = log( vx) = tan(x - y) 3- x Sec -x = y? log (sec x) 4-…

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

Q: /x[cosh?(2x²) – sinh²(2x²) ]dx is equal to

A: solution :let…

Q: S sin(4 + 5x) cos (5x – 4)dx

A: From the given problem: I=∫sin4+5xcos5x-4dx As we know that the trigonometric identity:…

Q: tan 2x dx 2. S (3+ln cos 2x)6

A:

Q: 1. ſ tan5 2x sec3 2x dx

A: Let,I=∫tan52xsec32xdxI=∫sin52xcos52x1cos32xdxI=∫sin52xcos82xdxI=∫sin42xcos82xsin(2x)dxusing…

Q: 5: - S cos(lnx).dx

A:

Q: 1. cos 3x dx

A: Since, the exact question was not specified so will answer very first question of it. Please…

Q: 106)Find the nth derivative of cosx cos2x cos3x AND ALSO FIND S dx sin?x

A: Cos2x = 2cos^2x -1

Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: Which of the following is the result of differentiating both sides of the equation xsin y = 2 ln x +…

A:

Q: evaluate the integral.

A:

Q: 2. * Evsluate O 4 | dx Evoluate @ 12-X

A:

Q: cos (In4x2) dx

A: Topic:- integration

Q: d/dx[(1-cosh(x))/(1+cosh(x))]

A:

Q: 50 6x sin dx e sec sec

A: The question seems to be wrong. I have made a few changes. The solution is as follows below:

Q: evaluate the integral.

A:

Q: S cos 8x dx

A:

Q: 3. C = cosh-1{sin¬1[tan log (3 – j8)]}

A:

Q: (1) S cos(7x + 5)dx

A: We need to integrate the given terms.  For this we will use substitution method.

Q: 1 dp- sin x cos x cos?,

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.