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UNIVERSIDAD DISTRITALFACULTAD TECNOLOGICA - ELECTRONICA
CALCULO INTEGRAL - TALLER # 4
(I) Hallar las siguientes integrales (sustitucion trigonometrica):
(1)∫ √
25−x2
xdx
(2)∫
1x2√
4−x2 dx
(3)∫
x3√
x2 − 4dx
(4)∫
x3√
1+x2 dx
(5)∫ √
x2−4x
dx
(6)∫
1x√
4x2+16dx
(7)∫
1(x2+3)3/2 dx
(8)∫
x√
16− 4x2dx
(9)∫ √
1−x2
x4 dx
(10)∫
x(x2+3)3/2 dx
(11)∫
x2√
4−x2 dx
(12)∫
e2x√
1 + e2xdx
(13)∫ √
1−x√x
dx
(14)∫
x(1−x2)3/2 dx
(15)∫
(x + 1)√
x2 + 2x + 2dx
(II) Completar el cuadrado y calcular la integral por sustitucion trigonometrica:
(1)∫
1√4x−x2 dx
(2)∫
x√x2+4x+8
dx
(3)∫
x2√
2x−x2 dx
(4)∫
x√x2−6x+5
dx
(III) Hallar la integral mediante fracciones simples(factores lineales)
(1)∫
14x2−9
dx
(2)∫
x+1x2+4x+3
dx
(3)∫
3x2−7x−2x3−x
dx
(4)∫
5−x2x2+x−1
dx
(5)∫
x2+12x+12x3−4x
dx
(6)∫
4x2+2x−1x3+x2 dx
(7)∫
x3−x+3x2+x−2
dx
(8)∫
2x−3(x−1)2
dx
(IV) Hallar la integral mediante fracciones simples(factores lineales y cuadraticos)
(1)∫
x2−1x3+x
dx
(2)∫
xx3−1
dx
(3)∫
2x2+x+8(x2+4)2
dx
(4)∫
x2
x4−2x2−8dx
(5)∫
x2−4x+7x3−x2+x+3
dx
(6)∫
x16x4−1
dx
(7)∫
x2+5x3−x2+x+3
dx
(8)∫
x2+x+3x4+6x2+9
dx
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