Integrais trigonométricas

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Universidade Tecnolo´gica Federal do Parana´
UTFPR — Campus Pato Branco
Lista 05 - Integrais: Poteˆncias trigonome´tricas
1. Resolva as seguintes integrais:
(a)
∫
sen3x cos2xdx
(b)
∫ 3pi
4
pi
2
sen5x cos3xdx
(c)
∫
sen2(pix) cos5(pix)dx
(d)
∫ pi
2
0
cos2θdθ
(e)
∫
cos4tdt
(f)
∫
(1 + cosθ)2dθ
(g)
∫ pi
2
0
sen2x cos2xdx
(h)
∫
cos2x tg3xdx
(i)
∫
sec2x tg xdx
(j)
∫
tg2xdx
(k)
∫
sec6xdx
(l)
∫ pi
3
0
tg5x sec4xdx
(m)
∫
tg3x sec xdx
(n)
∫
sen 8x cos 5x dx
(o)
∫
cos 7x cos 5x dx
1
Respostas!!
1. (a)
1
5
cos5x− 1
3
cos3x+ k
(b) − 11
384
(c)
1
3pi
sen3(pix)− 2
5pi
sen5(pix) +
1
7pi
sen7(pix) + k
(d)
pi
4
(e)
3
8
t+
1
4
sen(2t) +
1
32
sen(4t) + k
(f)
3
2
θ + 2senθ +
1
4
sen(2θ) + k
(g)
pi
16
(h)
1
2
cos2x− ln |cos x|+ k
(i)
1
2
tg2x+ k
(j) tg x− x+ k
(k)
1
5
tg5 t+
2
3
tg3 t+ tg t+ k
(l)
117
8
(m)
1
3
sec3 x− sec x+ k
(n) −1
6
cos 3x− 1
26
cos 13x+ k
(o)
1
4
cos 2x+
1
24
cos 12x+ k
Lista elaborada pelas Professoras Dr. Dayse Ferreira Batistus e Ms. Marieli Musial Tume-
lero
Digitac¸a˜o: Ms. Marieli Musial Tumelero
Configurac¸o˜es: Professora Ms. Marieli Musial Tumelero
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