Question

Integrate 1/x^2-4 dx

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ x^2-4 }dx\]

Answer 2

make partial fractions

Answer 3

i don't know partial fractions

Answer 4

couldn't i just make it;
\[(x^2-4)^{-1}\]

Answer 5

oh but then i would divide by zero

Answer 6

oh nevermind i would get:
\[\frac{ 1 }{ 0 }\]

Answer 7

\[\frac{ 1 }{x ^{2}-4 }=\frac{ 1 }{ \left( x-2 \right)\left( x+2 \right) }\]
\[=\frac{ A }{x-2 }+\frac{ B }{ x+2 }\]
\[1=A \left( x+2 \right)+B \left( x-2 \right)\]
equating coefficients of like powers.
0=A+B
1=2A-2B
solving for A and B
B=-A
1=2A+2A
A=1/4
B=-1/4

Answer 8

ok i kind of get it

Answer 9

\[\int\limits \frac{ dx }{x ^{2}-4}=\frac{ 1 }{ 4 } \int\limits \frac{ dx }{x-2 }-\frac{ 1 }{ 4 } \int\limits \frac{ dx }{x+2 }\]
solve it.

Answer 10

ok thanks

Answer 11

yw