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tr2os8x

tr2os8x

Answered question

2022-06-21

Compute
0 1 / 3 9 1 + 9 t 2 d t

Answer & Explanation

Patricia Curry

Patricia Curry

Beginner2022-06-22Added 15 answers

The substitution 3 t = u gives you the integral
0 1 9 1 + u 2 1 3 d u = 3 0 1 1 1 + u 2 d u
(note that u=0 for t=0 and u=1 for t = 1 / 3).
Yahir Tucker

Yahir Tucker

Beginner2022-06-23Added 8 answers

By decomposition in simple fractions, using complex numbers,
9 d t 1 + 9 t 2 = 9 2 ( 1 1 + i 3 t + 1 1 i 3 t ) d t = 9 6 i ( ln ( 1 + i 3 t ) ln ( 1 i 3 t ) ) = 3 arctan ( 3 t ) .

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