Lista_04_Integrais_Fracoes_Parciais

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Universidade Tecnolo´gica Federal do Parana´
UTFPR — Campus Pato Branco
Lista 04 - Integrais Utilizando Frac¸o˜es Parciais
1. Resolva as seguintes integrais:
(a)
∫
1
x2 − 4dx
(b)
∫
x
x2 − 4dx
(c)
∫
5x2 + 1
x− 1 dx
(d)
∫
x + 3
x2 − xdx
(e)
∫
x2 + 3
x2 − 9dx
(f)
∫
x
x2 − 5x + 6dx
(g)
∫
x + 3
(x− 1)2dx
(h)
∫
x2 + x + 1
x2 − x dx
(i)
∫
x3 + x + 1
x2 − 4x + 3dx
(j)
∫
1
x2 − x− 2dx
(k)
∫
x + 1
x(x− 1)(x− 2)dx
(l)
∫
x4 + x + 1
x3 − x dx
(m)
∫
2
(x− 1)2(x + 2)dx
(n)
∫
x + 3
x3 − 2x2 − x + 2dx
1
Respostas!!
1. (a)
1
4
ln
∣∣∣∣x− 2x + 2
∣∣∣∣+ k
(b)
1
2
ln |x2 − 4|+ k
(c) 6 ln |x− 1|+ 5
2
x2 + 5x + k
(d) −3 ln |x|+ 4 ln |x− 1|+ k
(e) x + 2 ln |x− 3| − 2 ln |x + 3|+ k
(f) −2 ln |x− 2|+ 3 ln |x− 3|+ k
(g) + ln |x− 1| − 4
x− 1k
(h) x− ln |x|+ 3ln|x− 1|+ k
(i)
x2
2
+ 4x− 3
2
ln |x− 1|+ 31
2
ln |x− 3|+ k
(j) −1
3
ln |x + 1|+ 1
3
ln |x− 2|+ k
(k) −1
6
ln |x|+ 3
10
ln |x− 2| − 2
15
ln |x + 3|+ k
(l)
x2
2
− ln |x|+ 3
2
ln |x− 1|+ 1
2
ln |x + 1|+ k
(m)
2
9
ln |x + 2| − 2
9
ln |x− 1| − 2
3(x− 1) + k
(n) −2 ln |x− 1|+ 1
3
ln |x + 1|+ 5
3
ln |x− 2|+ k
Lista elaborada pelos Professores Dr. Jose´ Donizetti de Lima e Ms. Marieli Musial Tumelero
Digitac¸a˜o: Larissa H. Vieira e Marieli Musial Tumelero
Configurac¸o˜es: Professora Ms. Marieli Musial Tumelero
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