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

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• MsMath
Lv 7

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)