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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