Question

integral of x²/x³+1​

Answer 1

integration x²/x³+1 dx

such that

x³+1=t

x²dx=dt

integration 1/tdx

log t +c

t= x³+1

log(x³+1)+c

Answer 2

Answer:

$→ \int \frac{ {x}^{2} }{( {x}^{3} + 1)} dx \\ Let\: \: ({x}^{3} + 1) = t \\ 3 {x}^{2} dx = dt \\ {x}^{2} dx = \frac{dt}{3} \\ → \frac{1}{3} \int \frac{dt}{t} = \frac{1}{3} log|t| +C = \frac{1}{3} log | {x}^{3} + 1 | +C$

• 1/3log|x³+1|+C is the right answer.