How do I evaluate #int_1^2(y + 5y^7)/y^3 dy#?

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How do I evaluate #int_1^2(y + 5y^7)/y^3 dy#?

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Answer 1 · 2015-01-27T13:28:09

I would break down the fraction as:
#int_1^2[y/y^3+5y^7/y^3]dy=#
#int_1^2[1/y^2+5y^4]dy=#
#int_1^2y^-2dy + int_1^2 5y^4dy=#
#=-1/y|_1^2# #+ 5y^5/5|_1^2=#
#=-1/y|_1^2# #+ y^5|_1^2=#
#(-1/2+1)+(2^5-1)=31.5#

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How do I evaluate #int_1^2(y + 5y^7)/y^3 dy#?

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