Loesungen/ Solutions

1

Integrate[Cos[x] + 2  -  Sin[x], {x, 0, 2  Pi}]

% // N

2

Integrate[x^4/4 + x^3/3 - 3 x^2 + 2  x - 4, x]

3

D[Integrate[(t^2 + 2  t) E^x, {x, 0, 1}], t] //  
      Simplify

Solve[
      D[Integrate[(t^2 + 2  t) E^x, {x, 0, 1}], t] == 
        0, {t}]

4

Integrate[Cos[2 x Pi], {x, 0, Pi}] // TrigReduce

Integrate[a Cos[2 x Pi  - Pi/2], {x, 0, Pi}] // 
      TrigReduce

5

Integrate[x^3 Log[x], {x, 1, E}] //  Simplify

% // N

6

Integrate[x Sin[x Pi], {x, 0, Pi}]

% // N

Integrate[x Sin[x Pi], {x, 0, Pi}] // TrigReduce

7

Integrate[(x^2 + 1)^2  Pi, {x, 0, 1}] //  Simplify

% // N

8

Integrate[x E^(-x^2), {x, 0, 1}]

% // N