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calculate the indefinite integral

2sec^2x dx

(cosx)/(sin^3x) dx

calculate the definite integral
interval pi/4, pi/12

csc2xcot2x dx

  • calculus - ,

    Well, I happen to know that the derivate of the tangent is sec^2 :)

    (cosx)/(sin^3x) dx

    Try f(x) = 1/sin^2 x
    f' = - 2 sin x cos x /sin^4 x
    see what happens?

    let u = 2 x
    then du = 2 dx
    and we have
    csc u cot u du/2 from u = pi/2 to pi/6

    (1/sin u)(cos u/sin u) du/2

    = (1/2) (cos u/sin^2 u) du

    try 1/sin u

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