Question

Oblicz całkę ułamków prostych

∫ (dx) / ( (4-3x)²)

Answer 1

 

∫[dx/(4 -3x)²] =

podstawienie 4 - 3x = t

zatem -3dx = dt --> dx = dt/(-3)

mamy więc

∫[dx/(4 -3x)²] = (-1/3)∫ dt/t² = (-1/3) ∫t⁻² dt = (-1/3)(-1/t) + c = 1/(3t) + c

czyli

∫[dx/(4 -3x)²] = 1/[ 3*(4 - 3x)]  + C