math

posted by .

what is the anti-derivative of cos^5x

  • math -

    cos^5θ = cos^4θ cosθ dθ
    = (1 - sin^2θ)^2 cosθ dθ
    = 1 - 2sin^2θ + sin^4θ cosθ dθ

    Now, note that if u = sinθ then du = cosθ dθ and we have

    1 - 2u^2 + u^4 du

    Easy peasie lemon-squeezy:

    u - 2/3 u^3 + 1/5 u^5 + C
    sinθ - 2/3 sin^3θ + 1/5 sin^5θ + C

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    find the area between the x-axis and the graph of the given function over the given interval: y = sqrt(9-x^2) over [-3,3] you need to do integration from -3 to 3. First you find the anti-derivative when you find the anti-derivative …
  2. anti derivative

    please help me find anti derivative of -sinx * cos^2x am i using integration by parts?
  3. calc

    i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given …
  4. Calculus

    Find the derivative of cos(sqrt(e^(x^3)cos(x)) I got -sin(sqrt(e^(x^3)cos(x))*((sqrt(e^(x^3)cos(x)) Do I just leave the e^(x^3)cosx alone since it's "e" or do I still have the find the derivative for it?
  5. Calculus 12th grade (double check my work please)

    1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) …
  6. calculus

    Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results …
  7. Calculus

    Find the anti derivative of the following: 1. u^-2(1-u^2+u^4)du 2. (sqrt(x)+ 3/x - 2e^(x))dx The anti derivative symbol is in front of the equations. Also need help on find f(x) so that it satisfies f'(x) = 1+e^x+1/x and f(1) = 3+e. …
  8. math

    How do I find the derivative of ⌠lnx ⌡π cos(e^(t))dt The question above is asking for the derivative of the integral cos(e^(t)) from pi to lnx
  9. Derivative

    Can you help me find the derivative of y= cos(x)/1+sin(x).. the / is a fraction bar. I have a hard time finding trig derivatives because I don't really know what the derivative of cos,sin ,or tan would be honestly.
  10. calculus

    Find the length of the curve given by the equation y= intergral from -pi to x of sqrt(cos(t)) dt for x between -pi and pi. I think I know to do this- at least part of it. I am using the fundamental theorem of calculus and the arc length …

More Similar Questions