Integral 2x + 5/(x² + 5x)² dx

^ tanda pangkat
(2x + 5) / (x² + 5x)² dx
= (2x + 5)(x² + 5x)^-2 dx
pakai integral substitusi
misalkan x² + 5x = u
(2x + 5)dx = du
dx = du/(2x+5)
maka
= (2x+5)u^-2 du/(2x+5)
= {(2x+5)/(2x+5)}u^-2 du
= u^-2 du
= (1 / -2+1)u^(-2+1) + C
= (1/-1) u^-1 + C
= -1u^-1 + C
= -1/u + C
= {-1/(x² + 5x)} + C