integral calculus

posted by .

evaluate integral by substitution (e^x-e^(-x))/(e^x+e^(-x))dx

  • integral calculus -

    Note that you have Integral(tanh(x) dx)
    = Integral (sinh(x)/cosh(x) dx)
    let u = cosh(x)
    du = sinh(x) dx

    and you have Integral(du/u) = ln(u) = ln(cosh(x)) = ln(e^x + e^-x) + C

    Equivalently, let u = e^x + e^-x
    Then du = e^x - e^-x du

    and you have du/u

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus II/III

    A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part …
  2. Math/Calculus

    How would I solve the following integral with the substitution rule?
  3. Calculus II

    Evaluate using u-substitution: Integral of: 4x(tan(x^2))dx Integral of: (1/(sqrt(x)*x^(sqrt(x))))dx Integral of: (cos(lnx)/x)dx
  4. Calculus

    I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5-(u^2))du I have a feeling I will be able to find …
  5. Calculus

    Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral.
  6. math

    Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6
  7. math

    Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral cos(9x) dx, u=9x
  8. calculus

    Use the indicated substitution to evaluate the integral integral 18sec(2x) tan(2x)dx, u=2x
  9. Calculus Please Help2

    Evaluate the integral by using substitution. Use an upper-case "C" for the constant of integration. integral x^5((x^6-2)^10)dx ty
  10. Question on Integration

    (i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts …

More Similar Questions