1-calculate-0-t-1-t-4-dt-2-calculate-0-1-t-1-t-4-dt-3-calculste-1-t-1-t-4-dt-

Question Number 42790 by maxmathsup by imad last updated on 02/Sep/18

1) c a l c u l a t e \int_{0}^{\infty} \frac{t}{1 + t^{4}} d t

2) c a l c u l a t e \int_{0}^{1} \frac{t}{1 + t^{4}} d t

3) c a l c u l s t e \int_{1}^{+ \infty} \frac{t}{1 + t^{4}} d t

Answered by MJS last updated on 03/Sep/18

\int \frac{t}{t^{4} + 1} d t = \frac{1}{2} \int \frac{d u}{u^{2} + 1} = \frac{1}{2} \arctan u =

= \frac{1}{2} \arctan t^{2} + C

(1) = \frac{π}{4}

(2) = (3) = \frac{π}{8}

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