A Geometria Analística

5) ∫x² + x-2 dx =   + + c =  x³ –  + c[pic 1][pic 2][pic 3][pic 4]

6) ∫ √x³ + ³√x² dx

∫ +1 dx ∫+1 dx [pic 5][pic 6]

∫ dx +  dx = 2√+ 3 ³√+ c[pic 7][pic 8][pic 9][pic 10]

7) ∫x³ + 6x+1 dx  ∫ + ∫ + 1 dx[pic 11][pic 12]

 + 3x² + x + c[pic 13]

8) x(1+2x) 4 dx

U=1 + 2x

Du=2 du=2dx  dx=du[pic 14]

U4 xdx  ∫* + c =  + C[pic 15][pic 16][pic 17]

9) ∫ (1-t)(2+t²) dt

∫2+t² – 2t-t³ dt

2∫dt + ∫ – ∫– ∫[pic 18][pic 19][pic 20]

2x+  -   -  [pic 21][pic 22][pic 23]

10)u(u²+2) ² du

∫u(u²+2)*(u²+2)du

∫u(u4+2u²+2u²+4)du

u(u4+4u²+4)du

∫u5+4u³+4u

∫  +  ∫  +  ∫  + c[pic 24][pic 25][pic 26]

 u6 + u4 + 2u² + c[pic 27]

21)[ ∫5.0] (6x²-4x+5)dx =   –   + 5x[pic 28][pic 29]

[ ∫5.0] 2x³-2x²+5x  [ ∫5.0] [2(5) ³-2(5) ²+5*5]-0

[ ∫5.0]  2*125-2*25+25=250-50+25=225

22) [ ∫3.1] (1+2x-4x³)dx = [ ∫3.1] x+- [pic 30][pic 31]

[ ∫3.1] x+x²-x4 [ ∫3.1] [3+3²-34]-1

3+9-82-1=12-83=71

23) [ ∫0.-1] x²-ex   [ ∫0.-1] [-2-ex]-[-1] ²-e-1 =-1- [pic 32]

24) [ ∫0.-2] (u5-u³+u²)du = [ ∫0.-2]  –   + [pic 33][pic 34][pic 35]

[ ∫0.-2]  -  +  = [ ∫0.-2]    -   -  =[pic 36][pic 37][pic 38][pic 39][pic 40][pic 41]