MCQ

**Choose the correct alternative from the following.**

`int "dx"/(("x - 8")("x + 7"))`=

#### Options

`1/15 log |("x" + 2)/("x - 1")|` + c

`1/15 log |("x + 8")/("x + 7")|` + c

`1/15 log |("x - 8")/("x + 7")|` + c

(x - 8)(x - 7) + c

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#### Solution

`1/15 log |("x - 8")/("x + 7")|` + c

**Explanation:**

Let I = `int "dx"/(("x - 8")("x + 7"))`

`= 1/15 int (15 * "dx")/(("x - 8")("x + 7"))`

`= 1/15 int (("x + 7") - ("x - 8"))/(("x - 8")("x + 7"))` dx

`= 1/15 (int 1/"x - 8" - int 1/"x + 7")` dx

`= 1/15 [log |"x - 8"| - log |"x + 7"|] + "c"`

`= 1/15 log |("x - 8")/("x + 7")|` + c

Is there an error in this question or solution?

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