CK-12-Calculus

7.3. Integration by Partial Fractions http://www.ck12.org

∫ 2

1

x^3 − 4 x^2 − 3 x+ 3

x^2 − 3 x dx=

∫ 2

1

[

(x− 1 )+−x (^26) −x+ 3 x^3

]

dx=

∫ 2

1

[

x− 1 −^1 x−x−^53

]

dx.

Integrating and substituting the limits,

=

[x 2

2 −x−ln

∣∣x∣∣−5ln∣∣x− 3 ∣∣]^2

1

=

( 4

2 −^2 −ln2−5ln1

)

−

( 1

2 −^1 −ln1−5ln2

)

=4ln2+^12.

Multimedia Links

For a complete partial fractions problem(19.0), see Integration by Partial Fractions, Just Math Tutoring (6:02)

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/599

and for integration using partial fractions and a rationalizing substitution(19.0), see Integration using Partial Fracti
ons and a rationalizing substitution, Just Math Tutoring (6:06).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/600

For an extensive presentation on integrating with partial fractions including the completing the square technique
(19.0)see Integration with partial fractions using various techniques, MIT Courseware (51:24).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/601