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Integrate t / (t^4 + 2)?

+1 vote
asked Dec 23, 2012 in Calculus by anonymous
    

1 Answer

0 votes

Solve by using u substitution as follows:

 = t^2
du = 2t * dt

t * dt / (2 + t^4) =>
(1/2) * du / (2 + u^2)

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

(1/2) * sqrt(2) * sec(x)^2 * dx / (2 + 2 * tan(x)^2)) =>
(1/2) * sqrt(2) * sec(x)^2 * dx / (2 * (1 + tan(x)^2)) =>
(1/2) * (1/2) * sqrt(2) * sec(x)^2 * dx / sec(x)^2 =>
(1/4) * sqrt(2) * dx

Integrate

(sqrt(2) / 4) * x + C

u = sqrt(2) * tan(x)
u / sqrt(2) = tan(x)
x = arctan(u / sqrt(2))

u = t^2

x = arctan(t^2 / sqrt(2))

(sqrt(2) / 4) * x + C =>>
(sqrt(2) / 4) * arctan(t^2 / sqrt(2)) + C

answered Dec 23, 2012 by Ytwsa ~Expert~ (1,082 points)

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