4 + sinh(3x) = 4 cosh(3x).

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: integral of x^2 sqrt(27+9x^2) dx

A: Formulae used:1. sec2x = 1+tan2x2. ∫secnx = secn-2x·tanxn-1 +n-2n-1∫secn-2x·dx + c3. ∫secx =…

Q: 3. J sinh(5x – 1) dx

A: Please refer the attached image for complete solution.

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: ЗсoshЗx dx| 4 + sinh3x 1/3

A: Given: 13∫3cosh3x4+sinh3xdx

Q: Solve 2 sinh(x)– cosh(x)= 5 by using the definition of the hyperbolic functions.

A: We know thatsinhθ=eθ-e-θ2coshθ=eθ+e-θ2

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: Evaluate the integral.

A:

Q: 14. √ √2-√x dx

A:

Q: 2 sinh x 2. Calculate the integral, dx. 5+6 cosh x

A:

Q: 5. 12 sec² (3x) dx 0.

A: We have to solve

Q: integral of sin^5(3x)cos^3(3x)dx

A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

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

A:

Q: Integrate tan -1 x dx without using integration by parts.

A: We will find the solution in the following step.

Q: Integral from 0 to 2pi of sin(2x) dx

A:

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: 2 dx

A: Solution

Q: Calculate the indefinite integral: ∫ sec2 x dx

A: Integration is the process of finding the anti-derivative function of a given function. The…

Q: integral of tan3xsec^4(3x) dx

A:

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: 3 dx V16-x²

A:

Q: Find the indefinite integral ∫coshx/sinhx  dx

A:

Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

A:

Q: Integral of 25 sqrt x^2-4/x^4 dx

A:

Q: sin“ (x)dx 4

A:

Q: Integral sinh2xcosh3xdx

A:

Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: Integral of sinh(e^lnarccot3x)dx/(1+9x^2)

A:

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

A: Given

Q: calculate the integral.

A: Given integral is We will use the following substitution to evaluate the integral

Q: Use integration by parts to find the indefinite integral ∫ln√( x2 − 4) dx

A: the integral given to us can be written as  ∫ln(x2-4)1/2 =12∫ln(x2-4)1/2 the formula used in by…

Q: tanh 2x In (cosh 2x)dx

A:

Q: X= sin 2tS In %3D Find dw 2- Cost

A:

Q: for dx

A: Given integration is : ∫exdx To find the value given integration by parts.

Q: x² sin 2x dx¸ Use integration by parts.

A:

Q: calculate the integral.

A:

Q: cosh(In x) dx

A:

Q: sin(5x)dx X sin

A:

Q: (7 – siny)y' = 3x2 + 2x

A:

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

A: To differentiate the given function.

Q: 2 cosh x+sinhx

A:

Q: (a) Sizl=1 dz.

A: Here we use property of analytic function.

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: Ssin(3x) sin(7x) dx

A:

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,

Q: Find the integral ∫dx / sinhx+2coshx.

A: Given Data The integral is ꭍdx/sinhx+2coshx.   Using the Weierstrass substitution in the given…