Use integration by parts to evaluate the definite integral: x(sec^2(5x)dx?

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  • MsMath
    Lv 7
    1 decade ago
    Favorite Answer

    Let u = x and dv = sec²(5x) dx, then

    du = dx and v = (1/5) tan(5x)

    uv - integral (vdu)

    = x(1/5) tan(5x) - integral ((1/5) tan(5x) dx)

    = (x/5) tan(5x) - (1/25) ln |sec(5x)| + C

  • Anonymous
    4 years ago

    Definite Integral By Parts

  • Anonymous
    4 years ago

    ? t e^{-t} dt The factors formulation is: ?u dv/dt dt = uv - ?v du/dt dt pick u = t, dv/dt = e^{-t} Then du/dt = a million and v = ?e^{-t} = -e^{-t}. for this reason the factors formulation will change into: ? t e^{-t} dt = [-te^{-t}] - ?(-e^{-t}) dt = [-te^{-t}] - [e^{-t}] comparing the sq. brackets with the bounds of 0 and three supplies -3e^-3 - (e^3 - a million) = a million - 4e^-3 it is your answer. desire it truly is effective :-) a million - 4/(e^3)

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