\require{AMSmath}

Hoe integreer je asin, acos en atan?

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f(x)=arcsin(x)

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$
\eqalign{
  & \int {\arcsin (x)\,\,dx = }   \cr
  & \int {\arcsin (x) \cdot 1\,\,dx = }   \cr
  & \arcsin (x) \cdot x - \int {x \cdot \frac{1}
{{\sqrt {1 - x^2 } }}} \,\,dx =   \cr
  & x \cdot \arcsin (x) - \int {\frac{x}
{{\sqrt {1 - x^2 } }}} \,\,dx =   \cr
  & x \cdot \arcsin (x) + \sqrt {1 - x^2 } + C  \cr}
$

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f(x)=arccos(x)

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$
\eqalign{
  & \int {\arccos (x)\,\,dx = }   \cr
  & \int {\arccos (x) \cdot 1\,\,dx = }   \cr
  & \arccos (x) \cdot x - \int {x \cdot  - \frac{1}
{{\sqrt {1 - x^2 } }}} \,\,dx =   \cr
  & x \cdot \arccos (x) + \int {\frac{x}
{{\sqrt {1 - x^2 } }}} \,\,dx =   \cr
  & x \cdot \arccos (x) - \sqrt {1 - x^2 }+ C  \cr}
$

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f(x)=arctan(x)

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$
\eqalign{
  & \int {\arctan (x)\,\,dx = }   \cr
  & \int {\arctan (x) \cdot 1\,\,dx = }   \cr
  & \arctan (x) \cdot x - \int {x \cdot \frac{1}
{{1 + x^2 }}\,\,} dx =   \cr
  & x \cdot \arctan (x) - \int {\frac{x}
{{1 + x^2 }}\,\,} dx =   \cr
  & x \cdot \arctan (x) - \frac{1}
{2}\ln (1 + x^2 )+ C \cr}
$

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