Evaluate the following integral. \int 2x(1-x^{-3})dx

Question
Applications of integrals
asked 2021-03-09
Evaluate the following integral.
\(\displaystyle\int{2}{x}{\left({1}-{x}^{{-{3}}}\right)}{\left.{d}{x}\right.}\)

Answers (1)

2021-03-10
\(\displaystyle\int{2}{x}{\left({1}-{x}^{{-{3}}}\right)}{\left.{d}{x}\right.}=\int{\left({2}{x}-{2}{x}^{{-{2}}}\right)}{\left.{d}{x}\right.}\)
\(\displaystyle={\left({2}{\frac{{{x}^{{{2}}}}}{{{2}}}}-{2}{\frac{{{x}^{{-{2}+{1}}}}}{{-{2}+{1}}}}\right)}+{c}\)
Hence, \(\displaystyle\int{2}{x}{\left({1}-{x}^{{-{3}}}\right)}{\left.{d}{x}\right.}={x}^{{{2}}}+{\frac{{{2}}}{{{x}}}}+{c}\)
0

Relevant Questions

asked 2020-11-05
Evaluate the following integral.
\(\displaystyle\int{x}^{{-{3}}}{\left({x}+{1}\right)}{\left.{d}{x}\right.}\)
asked 2021-01-15
Evaluate the integral.
\(\displaystyle\int{\left(\frac{{2}}{{x}^{{3}}}+\frac{{1}}{\sqrt{{x}}}\right)}{\left.{d}{x}\right.}\)
asked 2020-11-08
Evaluate the following integrals.
\(\displaystyle\int{\left({2}{x}^{{{3}}}-{x}^{{{2}}}+{3}{x}-{7}\right)}{\left.{d}{x}\right.}\)
asked 2021-02-14
Evaluate the following integral.
\(\displaystyle\int{\frac{{{x}}}{{\sqrt{{{x}-{4}}}}}}{\left.{d}{x}\right.}\)
asked 2020-12-13
Find the following integral.
\(\displaystyle\int{\left({\frac{{{2}}}{{{x}^{{{3}}}}}}+{\frac{{{1}}}{{\sqrt{{{x}}}}}}\right)}{\left.{d}{x}\right.}\)
asked 2020-12-24
Calculate the following integral.
\(\displaystyle\int{\left({x}-{\frac{{{2}}}{{{x}}}}-{2}{x}^{{{2}}}\right)}{\left.{d}{x}\right.}\)
asked 2020-10-19
Evaluate the integral.
\(\displaystyle\int{x}^{{{3}}}{\ln{{x}}}{\left.{d}{x}\right.}\)
asked 2021-03-07
Evaluate the integral.
\(\displaystyle\int\frac{{{3}-{x}}}{{\sqrt{{x}}}}{\left.{d}{x}\right.}\)
asked 2020-10-21
Evaluate the integral.
\(\displaystyle\int\sqrt{{x}}{\left({x}^{{3}}+\frac{{x}}{{2}}\right)}{\left.{d}{x}\right.}\)
asked 2020-11-09
Evaluate the integral.
\(\displaystyle\int\frac{{{x}^{{2}}-{1}}}{{{x}^{{2}}}}{\left.{d}{x}\right.}\)
...