1. (1) Calcular as integrais
R
(a) (x 2) (x 1) dx R: 1 x3 3 x2 + 2x
3 2
R (px+8) p 7 p 2
(b) dx R: 6 ( 6 x) + 12 ( 3 x)
R x1=3 p 7
p 3
(c) R (x ln x x) dx R: 1 x2 x ln x + x 2 ( x)
2 3
1
(d) 6x dx R: ln 6 6x
R 1
(e) px1 dx
1=p R: p 1 1 x1 p
R 2=3 p 2 p 5
(f) a x2=3 dx R: ( 3 a) x 3 ( 3 x)
R 1 p 5 p
(g) x2 +5 dx R: 1 5 arctan 1 x 5
5 5
R 2 +4 p p
(h) 3x2 +5 dx R: 3x 11 5 arctan 1 x 5
R x 5 5p
(i) p71 z2 dz R: arcsin 1 7z
7
R p
(j) pu2 9 du
2
R: 2 ln u + (u2 9)
R x+1
(k) x 4 dx R: x + 5 ln (x 4)
R (x px)2 1 4 p 3
(l) dx R: 1 x2 3 ( x) + x ln x
R (xm x n )2
x
2
(m) p
x
dx
R (eax ebx ) 1
1+a e
ax 1
1+b e
bx
(n) dx R:
R 1 ex p
ex
(o) px 2 dx R: 2 (x 2)
(2) Calcule as seguintes integrais
R p
(a) x2x 1 dx R: ln (x2 1)
R x2 9 1
(b) x2 +2x 3 dx R: x ln (x + 3) + ln (x 1)
R 1
4 4
(c) x(x2 +1) dx R:ln p x
2 (x +1)
R 1 1 x
(d) x(x+1)2 dx R: x+1 + ln x+1
R x p p p
(e) x3 +1 dx R: 1 ln x2 x+1 1
ln (x + 1) 6 3 + 3 3 arctan 3 2 x
1 1 1
R 6 3 3 3
(f) (x 1)(x x 2)(x 3) dx R: 2 ln (x 1) 2 ln (x 2) + 3 ln (x
1
2 3)
R
(g) (x+1)21(x+2)2 dx
1
R: x2 +3x+2 2x + 4 ln (x + 1) 4 ln (x + 2) + 6x ln (x + 1) 6x ln (x + 2) + 2x2 ln (x + 1) 2x2 ln (x + 2) + 3
(3) Calcular as seguintes integrais
R
(a) ex+10 dx R: ex+10
R
(b) ex1 dx R: ln 1
ex +1 e
x
R +1 1
(c) sin (x) cosm (x) dx R: ln(cos x)
m
cos x sin x
R 2
(d) lnx x dx R: 1
3 ln3 x
R p 1
p 3
(e) x 1 x2 dx R: 3 (1 x2 )
R
(f) p41 x2 dx R: arcsin 1 x
2
R 1
(g) p1+x2 dx R: arcsinhx
R p
(h) px1 1 dx
2
R: ln x + ( 1 + x2 )
Rp 1
p 1
p
(i) x2 2xdx R: 4 (2x 2) (x2 2x) 2 ln x 1 + (x2 2x)
R 1
p
(j) p1+2x x2 dx R: arcsin 1 2 (x 1)
2
R 10 1 11
(k) x (2x + 5) dx R: (22x 5) (2x + 5)
R 1
528 p
(l) pex 1 dx R: 2 arctan (ex 1)
R ln(tan ax)
(m) R sin ax1cos ax dx R: a
(n) x tan xdx
R
(o) ln x 1 dx
x+1
4
R:ln (x+1)(x 1) + ln x 1 x
x+1
(4) Calcular as seguintes integrais
1

2. 2
R
(a) R ln xdx R: x ln x x
(b) R x sin xdx R: sin x x cos x
(c) ex dx R: ex 1
R xx p x
px
e
(d) ln x dx
p R: 2 x ln x 4 x
R 2 x=2 1 1 1
(e) R x e dx R: 2x2 e 2 x 8xe 2 x + 16e 2 x
(f) R ln2 xdx R: ln2 x x 2x ln x + 2x
x
(g) R sin2 x dx R: x cot x + ln (sin x)
x
(h) e sin xdx 2
1
R: 1 ex cos x + 2 ex sin x
(5) Calcular
Rp
(a) ex + 2dx
R ex 1
(b) e2x +1 dx R : arctan (ex ) 2
R e3x
(c) e2x 1 dx R : ex + 2 ln (ex 1) 1 ln (ex + 1)
1
R 2
(d) sin x cos xex dx R : 10 e sin 2x 1 ex cos 2x + C
1 x
R x
5
(e) pee 1 dx
2x
R : arccosh (ex )
R x
(f) x2 dx R : ln1 2 (2x 2x x ln 2)
R 1
2
(g) p4x +1 dx
(6) Calcular as seguintes integrais
R
(a) sin2 x cos3 xdx R: 1 sin x 1
48 sin 3x
1
80 sin 5x
R dx 2
p8 2
p 1 1
p
(b) 2+sin x R: 3 3 arctan 3 3 tan 2 x + 3 3
R 1
(c) sin x+cos x dx
R 1+cos 2x
(d) dx R:ln (2 2 cos x) ln (2 cos x + 2) + 2 cos x
R sin x
dx
(e) sin(x+1) R: 1 ln (2 2 cos (x + 1)) 2 ln (2 cos (x + 1) + 2)
2
1
R 1
(f) sin3 x dx
R: 4 cos1 x 4 ln (2 cos x + 2)
2 ln (2 2 cos x) + 2 cos x + ln (2 2 cos x) cos2 x ln (2 cos x + 2) cos2 x