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topjm [15]
2 years ago
15

Find a formula for the function f(x) such that f′(x)=(ln(x))^2/x and f(2)=6

Mathematics
1 answer:
Rzqust [24]2 years ago
4 0
F(x)= ∫ln²x/x dx= ∫ln²xd(lnx) cause d(lnx)= (lnx)'dx=1/x dx
= ln³x/3 +C with C is constant
In addition, we have f(2)=6, so we have 6=ln³2/3+C
or C= 6- <span>ln³2/3
And f(x)= </span>ln³x/3+ <span> 6- </span><span>ln³2/3</span>
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