Lösungen

1

a

Integrate[x^2 Cos[x], x] + c

b

Integrate[Sin[2x] Cos[x/2], x] + c

c

Ln[x_]:=Log[x]

Integrate[Ln[2x], x] + c

Integrate[Ln[2x], {x,1,2}]

N[%]

d

Integrate[x^3 E^x, x] + c

Integrate[x^3 E^x, {x,0,1}]

N[%]

e

Integrate[Cos[x]^2, x] + c

Integrate[Cos[x]^2, {x,0, 2Pi}]

N[%]

2

a

Integrate[x Sqrt[x^2-4], x] + c

b

Integrate[Cos[x]^5 Sin[x], x] + c

c

Integrate[x Sqrt[1+x^2], x] + c

Integrate[x Sqrt[1+x^2], {x,0,1}]

N[%]

d

Integrate[Sqrt[4-x^2], x] + c

e

Integrate[1/Sqrt[4+x^2], x] + c

Integrate[1/Sqrt[4+x^2], {x,0, 1}]

N[%]

3

Integrate[Cos[a x] Sin[a x],{x,0,b}]^2

Integrate[Cos[a x]^2,{x,0,b}]

Integrate[Sin[a x]^2,{x,0,b}]

Integrate[Cos[a x]^2,{x,0,b}]*Integrate[Sin[a x]^2,{x,0,b}] //Expand

4

a

Integrate[x^2/(x^3-7),x] + c

b

Integrate[E^{2x}/(E^{2x}+7),x] + c

c

Integrate[(2 Cos[2x] + 4x + E^(-x)) /(Sin[2x] + 2x^2 - E^(-x) + 4),x] + c

d

Integrate[Cot[x],x] + c //Expand

5

a

Apart[1/(x(x-1))]

Integrate[1/(x(x-1)),x] + c

b

Apart[(x^4-16 x-3)/((x^2+1)(x-1)^2 (x+2))]

Integrate[(x^4-16 x-3)/((x^2+1)(x-1)^2 (x+2)),x] + c

c

Apart[(x^4-16 x-3)/((x^2+1)(x-1)^2)]

Integrate[(x^4-16 x-3)/((x^2+1)(x-1)^2),x] + c

d

Apart[(x^2-6 x-6)/(x^2(x^2+3 x+3))]

Integrate[(x^2-6 x-6)/(x^2(x^2+3 x+3)),x] + c

e

Apart[(90 x^3-76 x^2-25 x+19)/((2 x-1)(3 x+1)(5 x-3))]

Integrate[(90 x^3-76 x^2-25 x+19)/((2 x-1)(3 x+1)(5 x-3)),x] + c