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\require{AMSmath}
Hoe integreer je asin, acos en atan?
f(x)=arcsin(x)
$
\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}
$
f(x)=arccos(x)
$
\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}
$
f(x)=arctan(x)
$
\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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