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

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

Find the integral $\int\frac{( { x }^{ 2 } + 4x - 5)}{x+5}dx$

Options:

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

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

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

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

Correct Answer:

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

Explanation:

$\int\frac{( { x }^{ 2 } + 4x - 5)}{x+5}dx=\int\frac{(x+5)(x-1)}{(x+5)}dx$

$=\int x-1\,dx$

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