d 61. tanh(e*) = e* sech²(e*) dx

Q: 9. t² cosh 3t 10. t³ sinh t

A: solution of the given problem is below using laplace transformation...

Q: Find the indefinite integral sec* 7x dx.

A: To find the indefinite integral of ∫sec47xdx

Q: Find y′ if y = tanh−1(sinh x2).

A:

Q: (Tlog3(cosh z) + csch x) tanh x dx

A: Here we have to integrate the given Integral

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: 70ot(*) e*dx e2x +1

A:

Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: 101 Jzy cosu(x) + sinh(x)

A: Given differential equation:d2ydx2-y=coshx+sinhxTo find: General solution. Note:1 coshx=ex+e-x22…

Q: 76. Use integration by parts to obtain the formula VT=* dx = +VT=x + 1 dx. 1 – x?

A:

Q: 53. Find the value of 1 dx using weddle’s rule. 1+x?

A: Weddle's law is a formula for solving numerical integration.

Q: Ex Evaluote S 4e sinhx..dx

A:

Q: d VE evedt dx d -S Intdt dx 1

A:

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

A:

Q: 4(sinh 5. Evaluate 6 x) dx V1+x?

A: We use the well known formula for sinh^-1(x) = ln(x + sqrt(x^2+1)) and then integrate the…

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

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

Q: dx х V1-4 ln?х

A:

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

A:

Q: Show that e grows faster as x –→∞ than x" for any positive inte- ger n, even x'-000,000. (Hint: What…

A:

Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: Find e-ax dx } first integrating and then transforming result.

A: Here we find Laplace transform

Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: Find if y = e* In(sinh x) dx

A:

Q: Evaluate the indefinite integral. sec* (x)dx

A: We have to find the integral of sec^4(x)  Please see the explanation below

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: Use reduction formula to find (tanh" xdx 10

A:

Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

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

A:

Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: d 55. Vcosh x +1 (cosh x + 1)-/2 sinh x dx

A: Given The function is f(x)=cosh x +1 .

Q: Find the indefinite integral.

A: Use the substitution method and consider x2 as u. Differentiate both sides of u=x2 and substitute x2…

Q: Find the indefinite integral ∫sinh(1 − 2x) dx

A:

Q: Find the indefinite integral. S sinh (1 – 2x) dx

A:

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: Find the indefinite integral. ∫sec x/2 dx

A: Given ∫sec x/2 dx. We need to evaluate the above integral.

Q: Find the exact length from 1 to 2: y=((1/4)x^2)-(1/2)ln(x)

A: Find the exact length from 1 to 2: y=((1/4)x^2)-(1/2)ln(x)

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

A: Given

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: cosh(2x) = cosh?(x) + sinh² (x).

A:

Q: d y' of y= In(tanh2

A:

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: cosh(In x) dx

A:

Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: Find y' of y= In(tanh2x)

A:

Q: Sind dy forys(x) dx 3517X

A: y=(xx)3sin x

Q: dy y(ln y – In a + 1) dx 1 C = -ln C = -In Option 4 O option 2 1 C =-In

A: This question is based on solution of differential equation.

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

A: