To evaluate

Question

asked 2021-08-09

Evaluate the following integrals. Include absolute values only when needed.

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{\frac{{{\sin{{x}}}}}{{{1}+{\cos{{x}}}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{\frac{{{\sin{{x}}}}}{{{1}+{\cos{{x}}}}}}{\left.{d}{x}\right.}\)

asked 2021-08-11

Evaluate the following integrals. Check by differentiation.

\(\displaystyle\int{\left({x}^{{{4}}}-{4}{x}\right)}{\left.{d}{x}\right.}\)

\(\displaystyle\int{\left({x}^{{{4}}}-{4}{x}\right)}{\left.{d}{x}\right.}\)

asked 2021-08-12

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

\(\displaystyle\int{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{x}^{{{2}}}+{16}}}}}}\)

\(\displaystyle\int{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{x}^{{{2}}}+{16}}}}}}\)

asked 2021-08-11

Evaluate the following integrals.

\(\displaystyle\int{\frac{{{t}^{{{3}}}-{2}}}{{{t}+{1}}}}{\left.{d}{t}\right.}\)

\(\displaystyle\int{\frac{{{t}^{{{3}}}-{2}}}{{{t}+{1}}}}{\left.{d}{t}\right.}\)