What is the coefficient of n^2 in the sum of -5^4+4n^2-n+5 and 7n^4-5n^3-9n^2+3n+2
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Remember
for F(x) is the antiderivitive of f(x)
so find the antiderivitive of ((x+1)^2)/x
if we expand we get (x^2+2x+1)/x which simplifies to x+2+(1/x)
the anti-deritivive of x is (1/2)x^2
the antideritiveve of 2 is 2x
the antideritivieve of 1/x is ln|x|
F(x)=(1/2)x^2+2x+ln|x|+C
F(1)=(5/2)+ln1+C
F(2)=6+ln2+C
F(2)-F(1)=6+ln2+C-(5/2+ln1+C)
F(2)-F(1)=(7/2)+ln2
that is the answer
if you want is simplified or expanded it is about 4.1915
for F(x) is the antiderivitive of f(x)
so find the antiderivitive of ((x+1)^2)/x
if we expand we get (x^2+2x+1)/x which simplifies to x+2+(1/x)
the anti-deritivive of x is (1/2)x^2
the antideritiveve of 2 is 2x
the antideritivieve of 1/x is ln|x|
F(x)=(1/2)x^2+2x+ln|x|+C
F(1)=(5/2)+ln1+C
F(2)=6+ln2+C
F(2)-F(1)=6+ln2+C-(5/2+ln1+C)
F(2)-F(1)=(7/2)+ln2
that is the answer
if you want is simplified or expanded it is about 4.1915