asked 2021-11-10

Evaluate the definite integral.

\(\displaystyle{\int_{{-{\frac{{\pi}}{{{4}}}}}}^{{{\frac{{\pi}}{{{4}}}}}}}{\left({x}^{{{3}}}+{x}^{{{4}}}{\tan{{x}}}\right)}{\left.{d}{x}\right.}\)

\(\displaystyle{\int_{{-{\frac{{\pi}}{{{4}}}}}}^{{{\frac{{\pi}}{{{4}}}}}}}{\left({x}^{{{3}}}+{x}^{{{4}}}{\tan{{x}}}\right)}{\left.{d}{x}\right.}\)

asked 2021-08-15

Evaluate the indefinite integral.

\(\displaystyle\int{{\sec}^{{{3}}}{x}}{\tan{{x}}}{\left.{d}{x}\right.}\)

\(\displaystyle\int{{\sec}^{{{3}}}{x}}{\tan{{x}}}{\left.{d}{x}\right.}\)

asked 2021-08-14

Evaluate the integral.

\(\displaystyle\int{{\cot}^{{{3}}}{x}}{{\tan}^{{{4}}}{x}}{\left.{d}{x}\right.}\)

\(\displaystyle\int{{\cot}^{{{3}}}{x}}{{\tan}^{{{4}}}{x}}{\left.{d}{x}\right.}\)

asked 2021-08-17

Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)

\(\displaystyle\int{37}{e}^{{{74}{x}}}{\arctan{{\left({e}^{{{37}{x}}}\right)}}}{\left.{d}{x}\right.}\)

Inverse Trigonometric Forms (92): \(\displaystyle\int{u}{{\tan}^{{-{1}}}{u}}\ {d}{u}={\frac{{{u}^{{{2}}}+{1}}}{{{2}}}}{{\tan}^{{-{1}}}{u}}-{\frac{{{u}}}{{{2}}}}+{C}\)

\(\displaystyle\int{37}{e}^{{{74}{x}}}{\arctan{{\left({e}^{{{37}{x}}}\right)}}}{\left.{d}{x}\right.}\)

Inverse Trigonometric Forms (92): \(\displaystyle\int{u}{{\tan}^{{-{1}}}{u}}\ {d}{u}={\frac{{{u}^{{{2}}}+{1}}}{{{2}}}}{{\tan}^{{-{1}}}{u}}-{\frac{{{u}}}{{{2}}}}+{C}\)

asked 2021-05-14

Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)

\(\int37e^{74x}\arctan(e^{37x})dx\)

Inverse Trigonometric Forms (92): \(\int u\tan^{-1}u\ du=\frac{u^{2}+1}{2}\tan^{-1}u-\frac{u}{2}+C\)

\(\int37e^{74x}\arctan(e^{37x})dx\)

Inverse Trigonometric Forms (92): \(\int u\tan^{-1}u\ du=\frac{u^{2}+1}{2}\tan^{-1}u-\frac{u}{2}+C\)

asked 2021-11-16

Evaluate the following integral.

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

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

asked 2021-11-09

Evaluate the integral.

\(\displaystyle\int{x}{\sec{{x}}}{\tan{{x}}}{\left.{d}{x}\right.}\)

\(\displaystyle\int{x}{\sec{{x}}}{\tan{{x}}}{\left.{d}{x}\right.}\)