Question

O valor da integral indefinida ∫ $\frac{3}{x1n²3x}$ dx é:

a) $\frac{1}{x²1n3x}$ + C

b) $\frac{-3}{1n3x}$ + C

c) $\frac{3}{1n3x}$ + C

d) $\frac{x}{1n3x}$ + C

e) $\frac{1}{3x1nx}$ + C

Answer 1

$\int { \frac{3}{xln^2 (3x)}} \, dx \\\\ 3\int { \frac{1}{xln^2 (3x)}} \, dx \\\\ Fazemos\ u= ln(3x)\ e\ du=1/x \dx:\\\\ 3\int { \frac{1}{u^2}} \, du \\\\ A \ integral \ de \ 1/u^2=-1/u\\\\ Assim \ fica:\\\\ \frac{-3}{u} \ + \ C\\\\ Substituindo \ o \ valor\ de \ u=ln(3x):\\\\ \frac{-3}{ln(3x)} \ + \ C\\\\ Espero \ que \ tenha \ entendido!$