xdx/(x^2+3x+2) is equal to: (where c is an arbitrary constant) Option 1: -, x+1, +2, x+2, +c Option 2: x+1, -2, x+2, +c Option 3: -2, x+1, +2, x+2, +c Option 4: x+1, +2, x+2, +c

Answer: -, x+1, +2, x+2, +c. Solution: Factor the denominator as (x+1)(x+2) and use partial fractions: x/((x+1)(x+2)) = (-1)/(x+1) + 2/(x+2). Integrating term by term gives -, x+1, + 2, x+2, + c.

Calculus

Integrals

Easy

common

$\displaystyle\int \dfrac{xdx}{x^2+3x+2}$ is equal to:

(where $c$ is an arbitrary constant)

$-\log|x+1|+2\log|x+2|+c$

$\log|x+1|-2\log|x+2|+c$

$-2\log|x+1|+2\log|x+2|+c$

$\log|x+1|+2\log|x+2|+c$

✅ Correct Option: 1

Factor the denominator as $(x+1)(x+2)$ and use partial fractions:

$\dfrac{x}{(x+1)(x+2)} = \dfrac{-1}{x+1} + \dfrac{2}{x+2}$ .

Integrating term by term gives $-\log|x+1| + 2\log|x+2| + c$ .

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∫xdxx2+3x+2\displaystyle\int \dfrac{xdx}{x^2+3x+2}∫x2+3x+2xdx​ is equal to: (where ccc is an arbitrary constant)

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CUET Mathematics Past Year Questions (Topic-Wise)

$\displaystyle\int \dfrac{xdx}{x^2+3x+2}$ is equal to:

(where $c$ is an arbitrary constant)