Math

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Evaluate the integral of
(secx)^2 * (tanx)^3 *dx


I started out with letting u=secx and du=secx*tanx*dx , but then I am kind of stuck because I don't know how to factor out just secx*tanx?

The answer in the book said that it is (1/4)(tanx)^4 + C.

  • Math -

    Nice try. But you need to explore other options:

    u = tan(x)
    du = sec^2(x) dx

    ∫sec^2x tan^3x dx
    = ∫u^3 du
    = 1/4 u^4
    = 1/4 tan^4(x) + C

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