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Fill in the Blank. ∫x2+x-6(x - 2)(x - 1)dx=x + ______ + c - Mathematics and Statistics

Fill in the Blanks

Fill in the Blank.

`int ("x"^2 + "x" - 6)/(("x - 2")("x - 1")) "dx" = "x"` + ______ + c

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Solution

`int ("x"^2 + "x" - 6)/(("x - 2")("x - 1")) "dx" = "x"` + 4 log |x - 1| + c

Explanation:

`int ("x"^2 + "x" - 6)/(("x - 2")("x - 1")) "dx" = int(("x + 3")("x - 2"))/(("x - 2")("x - 1"))`dx

`= int ("x + 3")/("x - 1")` dx

`= int (("x - 1") + 4)/("x - 1")` dx

`= int (1 + 4/"x - 1")` dx

= x + 4 log |x - 1| + c

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 2.2 | Page 138
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