Evaluate the following integral. \int x^{-3}(x+1)dx

Evaluate the following integral. \int x^{-3}(x+1)dx

Question
Applications of integrals
asked 2020-11-05
Evaluate the following integral.
\(\displaystyle\int{x}^{{-{3}}}{\left({x}+{1}\right)}{\left.{d}{x}\right.}\)

Answers (1)

2020-11-06
\(\displaystyle\int{x}^{{-{3}}}{\left({x}+{1}\right)}{\left.{d}{x}\right.}=\int{\left({x}^{{-{2}}}+{x}^{{-{3}}}\right)}{\left.{d}{x}\right.}\)
\(\displaystyle={\frac{{{x}^{{-{2}+{1}}}}}{{-{2}+{1}}}}+{\frac{{{x}^{{-{3}+{1}}}}}{{-{3}+{1}}}}+{c}\)
Hence, \(\displaystyle\int{x}^{{-{3}}}{\left({x}+{1}\right)}{\left.{d}{x}\right.}=-{\frac{{{1}}}{{{x}}}}-{\frac{{{1}}}{{{2}{x}^{{{2}}}}}}+{c}\)
0

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