Evaluate the integral. int(x^2-1)/(x^2)dx

Evaluate the integral. int(x^2-1)/(x^2)dx

Question
Applications of integrals
asked 2020-11-09
Evaluate the integral.
\(\displaystyle\int\frac{{{x}^{{2}}-{1}}}{{{x}^{{2}}}}{\left.{d}{x}\right.}\)

Answers (1)

2020-11-10
Given That
\(\displaystyle\int\frac{{{x}^{{2}}-{1}}}{{{x}^{{2}}}}{\left.{d}{x}\right.}\)
\(\displaystyle=\int{\left({1}-\frac{{1}}{{x}^{{2}}}\right)}{\left.{d}{x}\right.}\)
\(\displaystyle=\int{\left.{d}{x}\right.}-\int\frac{{1}}{{{x}^{{2}}}}{\left.{d}{x}\right.}\)
\(\displaystyle={x}-{\left[\frac{{{x}^{{-{2}+{1}}}}}{{-{2}+{1}}}\right]}+{c}\)
\(\displaystyle={x}+\frac{{1}}{{x}}+{c}\)
\(\displaystyle\therefore\int\frac{{{x}^{{2}}-{1}}}{{{x}^{{2}}}}{\left.{d}{x}\right.}={x}+\frac{{1}}{{x}}+{c}\)
0

Relevant Questions

asked 2021-05-29
Evaluate the following integral: \(\int \frac{x+3}{x-1}dx\)
asked 2021-05-26
use the table of integrals to evaluate the following integral.
\(\int 3x \sqrt{6x-x^2}dx\)
asked 2021-05-28
Evaluate the following integral.
\(\int \frac{3x^{2}+\sqrt{x}}{\sqrt{x}}dx\)
asked 2021-05-23
Use a change of variables to evaluate the following integral.
\(\int-(\cos^{7}x-5\cos^{5}x-\cos x)\sin x dx\)
asked 2021-05-23
Evaluate each of the following integrals.
\(\int\frac{e^{x}}{1+e^{x}}dx\)
asked 2021-05-21
Evaluate the integral.
\(\int_{1}^{2}\frac{(x+1)^{2}}{x}dx\)
asked 2021-05-11
Evaluate the following integral: \(\int \frac{(y-3)}{y^{2}-6y+1}\)
asked 2021-05-30
Evaluate the following integral: \(\int\frac{vdv}{6v^{2}-1}\)
asked 2021-05-23
Find the indefinite integral \(\int \ln(\frac{x}{3})dx\) (a) using a table of integrals and (b) using the Integration by parts method.
asked 2021-05-11
Evaluate the surface integral.
\(\int \int_s (x^2z +y^2z)dS\)
S is the hemisphere \(x^2 +y^2 + z^2 = 4, z \geq 0\)
...