Question

Evaluate Integral of ((cosh x) / (9-sinh^2(x))) dx

Limits: a=ln7, b= ln9

Answer #1

1) Verify the following identities
a) cosh2(x) - sin2h(x) = 1
b) cosh(x+y) = cosh(x) cosh(y) + sinh(x) sinh(y)
2) Show that
d/dx (csch(x)) = -csch(x) coth(x)

Evaluate the following indefinite integral: ∫x^2/√(16+x^2
)dx
Evaluate the following indefinite integral: ∫xe^2x dx

Evaluate the integral: ∫8x^2 / √9−x^2 dx
(A) Which trig substitution is correct for this integral?
x=9sec(θ)
x=3tan(θ)
x=9tan(θ)
x=3sin(θ)
x=3sec(θ)
x=9sin(θ)
(B) Which integral do you obtain after substituting for x and
simplifying?
Note: to enter θθ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?

evaluate the integral ∫(x+2)/(x²+4) dx

Evaluate the integral: ∫27√x^2−9 / x^4 dx
(A) Which trig substitution is correct for this integral?
x=3tan(θ)
x=27sin(θ)
x=3sin(θ)
x=9tan(θ)
x=3sec(θ)
x=9sec(θ)
(B) Which integral do you obtain after substituting for xx and
simplifying?
Note: to enter θθ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?

1) show that
tanh-1(x) = 1/2 ln (1+x/1-x)
2) show that
a) d/dx (cosh-1(x)) = 1/sqrt x2-1
b) d/dx (tanh-1(x)) = 1/1-x2
3) verify that y = A cosh(3x) + B sinh(3x) is a solution to the
equation y''-9y = 0

9) find the integral using trigonometric substituition
integral of ((x^2)/ sqroot(9 - x^2)) dx

Evaluate the integral from -1 to 2 for (6x + 10 |x| ) dx

Use Romberg integration to evaluate the integral of e^(-x^2 )
between the limits a=1 and b=2.5. Use the initial h=b-a. Find the
integral to an error of order O(h^6).

(#9) evaluate integral SQRT(16x^2-1)dx using trigonometric
substitution

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