Find the integral \(\int\frac{( { x }^{

CUET Preparation Today

Start Free Mocks

Home Questions 52JKMZUCSF

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

Find the integral $\int\frac{( { x }^{ 2 } - 5x + 6)}{x-3}dx$

Options:

$\frac{ { x }^{ 2 } }{2} - 2x+c$

$\frac{ { -x }^{ 2 } }{2} - 2x+c$

$\frac{ { x }^{ 2 } }{2} + 2x+c$

$\frac{ { -x }^{ 2 } }{2} + 2x+c$

Correct Answer:

$\frac{ { x }^{ 2 } }{2} - 2x+c$

Explanation:

$\int\frac{( { x }^{ 2 } - 5x + 6)}{x-3}dx=\int\frac{(x-3)(x-2)}{(x-3)}dx$

$\int (x-2)dx=\frac{ { x }^{ 2 } }{2} - 2x+c$