calc

posted by .

also:

integral of tan^(-1)y dy

how is integration of parts used in that?

You write:

arctan(y)dy = d[y arctan(y)] -
y d[arctan(y)]

Here we again have used the product rule:

d(fg) = f dg + g df

You then use that:

d[arctan(y)] = 1/(1+y^2) dy

So, the integral becomes:

y arctan(y) - Integral of y/(1+y^2) dy


And:

Integral of y/(1+y^2) dy =

1/2 Log[1+y^2] + const.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. limiting position of the particle

    A particle moves along the x axis so that its position at any time t>= 0 is given by x = arctan t What is the limiting position of the particle as t approaches infinity?
  2. Calculus

    Note that pi lim arctan(x ) = ---- x -> +oo 2 Now evaluate / pi \ lim |arctan(x ) - -----| x x -> +oo \ 2 / I'm not exactly sure how to attempt it. I have tried h'opital's rule but I don't believe you can use it here. Any help …
  3. calculus

    Let f be a function defined by f(x)= arctan x/2 + arctan x. the value of f'(0) is?
  4. calculus

    h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ?
  5. calculus

    h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ?
  6. Calc

    Evaluate the integral (3x+4)/[(x^2+4)(3-x)]dx a. (1/2)ln(x^2+4) + ln|3-x| + C b. (1/2)arctan(x/2) + ln|3-x| + C c. (1/2)arctan(x/2) - ln|3-x| + C d. ln|(sqrt(x^2+4)/(3-x))| + C e. None of the above
  7. precal

    The values of x that are solutions to the equation cos^(2)x=sin2x in the interval [0, pi] are a. arctan(1/2) only b. arctan(1/2) and pi c. arctan(1/2) and 0 d. arctan(1/2) and (pi/2) e. arctan(1/2), o, and (pi/2)
  8. check my arctan please

    arctan(1/12)= 4.763 rounded to the nearest tenth degree, which is 4.8?
  9. calc

    find this value. tan(arctan(3)) how do ifind arctan 3
  10. Calculus prince@18

    let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that …

More Similar Questions