HELP!

Co ja źle liczę, że to zadanie wychodzi totalnie bez sensu?! :(

"4. obliczyć granicę" ~ lim from x toward +infinity {{int from x to x+1 {t cdot ln{(t^2+1)}dt}} over {x^2+1}}
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"Rozbijamy całkę na dwie"
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lim from x toward +infinity {{- int from c to x {t cdot ln(t^2+1)dt} + int from c to x+1 {t cdot ln(t^2+1)dt}} over {x^2+1}}
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"Korzystamy z twierdzenia d'Hospitala:"
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lim from x toward +infinity {{-(x cdot ln(x^2+1))+(x+1) cdot ln((x+1)^2+1)} over {2x}} = lim from x toward +infinity {{-x cdot ln(x^2+1)+x cdot ln(x^2+2x+2)+ln} over {2x}}
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"Korzystamy z twierdzenia d'Hospitala po raz drugi:"
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lim from x toward +infinity {{-ln(x^2+1)+ {2x^2} over {x^2+1} + ln(x^2+2x+2) - {2x^2+2x} over {x^2+2x+2} + {2x+2} over {x^2+2x+2}} over {2}}
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"co po przekształceniach daje coś w tym guście:"
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lim from x toward +infinity {{-ln(x^2+1)+ln(x^2+2x+2) + {4x^3+4x^2+2} over {x^4+2x^3+3x^2+2x+2}} over {2}}

??????

Moje rozw.:

"4. obliczyć granicę" ~ lim from x toward +infinity {{int from x to x+1 {t cdot ln{(t^2+1)}dt}} over {x^2+1}}
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"Rozbijamy całkę na dwie"
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lim from x toward +infinity {{- int from c to x {t cdot ln(t^2+1)dt} + int from c to x+1 {t cdot ln(t^2+1)dt}} over {x^2+1}}
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"Korzystamy z twierdzenia d'Hospitala:"
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lim from x toward +infinity {{-(x cdot ln(x^2+1))+(x+1) cdot ln((x+1)^2+1)} over {2x}} = lim from x toward +infinity {{-x cdot ln(x^2+1)+x cdot ln(x^2+2x+2)+ln(x^2+2x+2)} over {2x}}
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lim from x toward +infinity {{x cdot [ln(x^2+2x+2)-ln(x^2+1)] + ln(x^2+2x+2)} over {2x}} =
lim from x toward +infinity {{x cdot ln({x^2+2x+2} over {x^2+1}) + ln(x^2+2x+2)} over {2x}}
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"Rozbijamy granice na dwie i w drugiej korzystamy z de l'Hospitala"
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lim from x toward +infinity {{ln({x^2+2x+2} over {x^2+1})} over {2}} + lim from x toward +infinity {{2x+2} over {2 cdot (x^2+2x+2)}}  = 0