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Question:

The integral ∫(2x³-1)/(x⁴+x)dx is equal to?

loge|x³+1/x|+C

1/2loge(x³+1)²/|x³|+C

loge|x³+1|/x²+C

1/2loge|x³+1|/x²+C

Solution:

Correct option is A. loge|x³+1/x|+C
∫(2x³-1)/(x⁴+x)dx
∫(2x-1/x²)/(x²+1/x)dx
x²+1/x=t
(2x-1/x²)dx=dt
∫dt/t=ln(t)+C=ln(x²+1/x)+C