1. Integrating Quadratic
Denominators
1 2 dx 2 dx
a x a x a x
dx dx
2 2 2
x a x a x a
2. Integrating Quadratic
Denominators
1 2 dx 2 dx
a x a x a x done via
dx dx
2 2 2 partial fractions
x a x a x a
3. Integrating Quadratic
Denominators
1 2 dx 2 dx 1 a x c
log
a x a x a x done via
2a a x
partial fractions 1 log x a c
dx dx
2 2 2
x a x a x a
2a x a
4. Integrating Quadratic
Denominators
1 2 dx 2 dx 1 a x c
log
a x a x a x done via
2a a x
partial fractions 1 log x a c
dx dx
2 2 2
x a x a x a
2a x a
dx 1 1 x
3 2 2 tan c
a x a a
5. Integrating Quadratic
Denominators
1 2 dx 2 dx 1 a x c
log
a x a x a x done via
2a a x
partial fractions 1 log x a c
dx dx
2 2 2
x a x a x a
2a x a
dx 1 1 x
3 2 2 tan c
a x a a
dx 1 x
4 sin c
a x
2 2
a
6. Integrating Quadratic
Denominators
1 2 dx 2 dx 1 a x c
log
a x a x a x done via
2a a x
partial fractions 1 log x a c
dx dx
2 2 2
x a x a x a
2a x a
dx 1 1 x
3 2 2 tan c 5
dx
x2 a2
log x x 2 a 2 c
a x a a
dx 1 x
4 sin c
a x
2 2
a
7. Integrating Quadratic
Denominators
1 2 dx 2 dx 1 a x c
log
a x a x a x done via
2a a x
partial fractions 1 log x a c
dx dx
2 2 2
x a x a x a
2a x a
dx 1 1 x
3 2 2 tan c 5
dx
x2 a2
log x x 2 a 2 c
a x a a
4
dx
sin 1 x
c 6
dx
a2 x2
log x a 2 x 2 c
a x
2 2
a