Určitý integrál
Ahoj, poradí mi někdo s tímto příkladem? nevím, jak se to počítá.
http://www.wolframalpha.com/input/?i=integral+%281%2Bcos^4%28x%29%29%2F%28sin^3%28x%29%29
http://www.wolframalpha.com/input/?i=integral+%281%2Bcos^4%28x%29%29%2F%28sin^3%28x%29%29
Odpovědi
Diskuze
∫f(x)*dx = F(x)+C (neurčitý integrál)
meze(od 'a' do 'b'); ∫f(x)*dx = F(b)-F(a)
cos(x) = t
–sin(x) dx = dt
=1/sin3x + cos2x*cos2x/sin3x =
=1/sin3x + cos2x*(1-sin2x)/sin3x =
=1/sin3x + cos2x/sin3x - cos2x/sinx =
=1/sin3x + (1-sin2x)/sin3x - (1-sin2x)/sinx =
=2/sin3x - 2/sinx + sinx = ...
http://www.wolframalpha.com/input/?i=integrate+2%2F%28sinx%29%5E3
∫2/sinx dx = integrate 2/sinx =
http://www.wolframalpha.com/input/?i=integrate+2%2Fsinx
∫sinx dx = -cosx + C