\require{AMSmath}

6. Enkele standaardintegralen

\eqalign{   & \int {\frac{1} {{\sin x}}dx}  = \ln \frac{{1 - \cos x}} {{\left| {\sin x} \right|}}\,\,(1.8)  \cr   & \int {\frac{{dx}} {{a^2  + b^2 x^2 }} = \frac{1} {{ab}}\arctan \frac{{bx}} {a}} \,\,\,(1.19)  \cr   & \int {\sin mx \cdot \cos nx\,dx =  - \frac{{\cos (m - n)x}} {{2(m - n)}}}  - \frac{{\cos (m + n)x}} {{2(m + n)}}\,\,(m^2  \ne n{}^2)\,\,(1.16)  \cr   & \int {\sqrt {a^2  + x^2 } } dx = \frac{x} {2}\sqrt {a^2  + x^2 }  + \frac{{a^2 }} {2}\ln \left( {x + \sqrt {a^2  + x^2 } } \right)\,\,\left( {a \in {R}^ +  } \right)\,\left( {1.25} \right)  \cr   & \int {\frac{1} {{a^2  - b^2 x^2 }}} \,dx = \frac{1} {{2ab}}\ln \left| {\frac{{a + bx}} {{a - bx}}} \right|\,\,\,\left( {a,b \in {R}^ +  } \right)\,\,\left( {1.20} \right)  \cr   & \int {\frac{{dx}} {{\sqrt {a^2  - x^2 } }}}  = \arcsin \left( {\frac{x} {a}} \right)\,\,\left( {a \in {R}^ +  } \right)\left( {1.21} \right) \cr}

• Standaardintegraal ?
• Standaardintegraal 1.24

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