RespostasLista10Exercicio1Calculo1 - Gabarito Integrais

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Universidade Veiga de Almeida
Curso: Ba´sico das Engenhrarias
Disciplina: Ca´lculo Diferencial e Integral I
Professora: Adriana Nogueira
Respostas da 10a Lista de Exerc´ıcios
Exerc´ıcio 1:
(a)
∫
dx
3x+ 2
=
1
3
ln|3x+ 2|+ c
(b)
∫
dx
ax+ b
=
1
a
ln|ax+ b|+ c
(c)
∫
(5x− 3)2dx = (5x− 3)
3
15
+ c
(d)
∫
x2dx
cos2(x3)
=
1
3
tg(x3) + c
(e)
∫
xe(2x
2+1)dx =
1
4
e(2x
2+1) + c
(f)
∫
x
√
x2 + 1dx =
1
3
(x2 + 1)3/2 + c
(g)
∫
lnxdx
x
=
(lnx)2
2
+ c
(h)
∫
arctgxdx
1 + x2
=
(arctgx)2
2
+ c
(i)
∫
xcos(x2)dx =
sen(x2)
2
+ c
1
(j)
∫
sec2xdx√
1 + 2tgx
=
√
1 + 2tgx+ c
(k)
∫
sen
√
xdx√
x
= −2cos(√x) + c
(l)
∫
xe(−x
2)dx =
−1
2
e(−x
2) + c
(m)
∫ √1 +√x
x
dx =
4
3
(1 +
√
x)3/2 + c
(n)
∫ [1 + ln(x2)]2
x
dx =
(1 + ln(x2))3
6
+ c
(o)
∫
e
1
x
x2
dx = −e 1x + c
(p)
∫
dx
(4x+ 5)5
=
−1
16(4x+ 5)4
+ c
(q)
∫
dx√
7x+ 9
=
2
7
√
7x+ 9 + c
(r)
∫
cos 3
√
x
3
√
x2
dx = 3sen( 3
√
x) + c
2