Annex: Integrals of trigonometric inverse functions

format_list_bulleted Contenido keyboard_arrow_down

ImprimirCitar

The following is a list of integrals of trigonometric inverse functions.

{displaystyle int arcsin {frac {x}{c}},dx=xarcsin {frac {x}{c}}+{sqrt {c^{2}-x^{2}}}}

{displaystyle int xarcsin {frac {x}{c}},dx=left({frac {x^{2}}{2}}-{frac {c^{2}}{4}}right)arcsin {frac {x}{c}}+{frac {x}{4}}{sqrt {c^{2}-x^{2}}}}

{displaystyle int x^{2}arcsin {frac {x}{c}},dx={frac {x^{3}}{3}}arcsin {frac {x}{c}}+{frac {x^{2}+2c^{2}}{9}}{sqrt {c^{2}-x^{2}}}}

{displaystyle int arccos {frac {x}{c}},dx=xarccos {frac {x}{c}}-{sqrt {c^{2}-x^{2}}}}

{displaystyle int xarccos {frac {x}{c}},dx=left({frac {x^{2}}{2}}-{frac {c^{2}}{4}}right)arccos {frac {x}{c}}-{frac {x}{4}}{sqrt {c^{2}-x^{2}}}}

{displaystyle int x^{2}arccos {frac {x}{c}},dx={frac {x^{3}}{3}}arccos {frac {x}{c}}-{frac {x^{2}+2c^{2}}{9}}{sqrt {c^{2}-x^{2}}}}

{displaystyle int arctan {frac {x}{c}},dx=xarctan {frac {x}{c}}-{frac {c}{2}}ln(c^{2}+x^{2})}

{displaystyle int xarctan {frac {x}{c}},dx={frac {c^{2}+x^{2}}{2}}arctan {frac {x}{c}}-{frac {cx}{2}}}

{displaystyle int x^{2}arctan {frac {x}{c}},dx={frac {x^{3}}{3}}arctan {frac {x}{c}}-{frac {cx^{2}}{6}}+{frac {c^{3}}{6}}ln {c^{2}+x^{2}}}

{displaystyle int x^{n}arctan {frac {x}{c}},dx={frac {x^{n+1}}{n+1}}arctan {frac {x}{c}}-{frac {c}{n+1}}int {frac {x^{n+1}dx}{c^{2}+x^{2}}}qquad {mbox{(para }}nneq -1{mbox{)}}}

{displaystyle int mathrm {arccot} ,{frac {x}{c}},dx=x,mathrm {arccot} ,{frac {x}{c}}+{frac {c}{2}}ln(c^{2}+x^{2})}

{displaystyle int x,mathrm {arccot} ,{frac {x}{c}},dx={frac {c^{2}+x^{2}}{2}},mathrm {arccot} ,{frac {x}{c}}+{frac {cx}{2}}}

{displaystyle int x^{2},mathrm {arccot} ,{frac {x}{c}},dx={frac {x^{3}}{3}},mathrm {arccot} ,{frac {x}{c}}+{frac {cx^{2}}{6}}-{frac {c^{3}}{6}}ln(c^{2}+x^{2})}

{displaystyle int x^{n},mathrm {arccot} ,{frac {x}{c}},dx={frac {x^{n+1}}{n+1}},mathrm {arccot} ,{frac {x}{c}}+{frac {c}{n+1}}int {frac {x^{n+1}dx}{c^{2}+x^{2}}}qquad {mbox{(para }}nneq -1{mbox{)}}}

Contenido relacionado

Más resultados...