Question

Calcule a integral ∫1/ x²+3x−10dx.

Answer 1

$\int\ {\frac{1}{ x^{2} +3x-10} } \, dx = \int\ { \frac{1}{ (x^{2} +3x+ \frac{9}{4})-\frac{9}{4}-10 } } \, dx = \int\ { \frac{1}{ ( x+ \frac{3}{2})^{2}-\frac{49}{4} } } \, dx=$
$\int\ { \frac{1}{ ( x+ \frac{3}{2})^{2}- \sqrt{(\frac{49}{4})^{2} } } } \, dx$

u= $x+ \frac{3}{2}$
a= $\sqrt{ \frac{49}{4} }$= $\frac{7}{2}$

$\frac{1}{2. \frac{7}{2} }$.ln$| \frac{x+ \frac{3}{2}- \frac{7}{2} }{x+ \frac{3}{2} + \frac{7}{2} } |$ =

$\frac{1}{7 } .ln| \frac{x- 2}{x+5} } | + c$