To evaluate:

asked 2021-05-26

use the table of integrals to evaluate the following integral.

\(\int 3x \sqrt{6x-x^2}dx\)

\(\int 3x \sqrt{6x-x^2}dx\)

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 2021-10-20

Evaluate the following integrals.

\(\displaystyle\int{\frac{{{1}}}{{{x}+\sqrt{{{x}}}}}}{\left.{d}{x}\right.}\)

\(\displaystyle\int{\frac{{{1}}}{{{x}+\sqrt{{{x}}}}}}{\left.{d}{x}\right.}\)

asked 2021-11-07

Use a table of integrals to evaluate the following indefinite integral.

\(\displaystyle\int{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{x}^{{{2}}}-{25}}}}}}\)

\(\displaystyle\int{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{x}^{{{2}}}-{25}}}}}}\)

asked 2021-11-07

Use a table of integrals to evaluate the following indefinite integral.

\(\displaystyle\int{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{x}^{{{2}}}-{6}{x}}}}}},{x}{>}{6}\)

\(\displaystyle\int{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{x}^{{{2}}}-{6}{x}}}}}},{x}{>}{6}\)

asked 2021-11-08

Use a table of integrals to evaluate the following indefinite integral.

\(\displaystyle\int{x}^{{{2}}}{e}^{{{5}{x}}}{\left.{d}{x}\right.}\)

\(\displaystyle\int{x}^{{{2}}}{e}^{{{5}{x}}}{\left.{d}{x}\right.}\)

asked 2021-11-09

Use a table of integrals to evaluate the following indefinite integrals.

\(\displaystyle\int{\sin{{3}}}{x}{\cos{{2}}}{x}{\left.{d}{x}\right.}\)

\(\displaystyle\int{\sin{{3}}}{x}{\cos{{2}}}{x}{\left.{d}{x}\right.}\)