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MHTCET 11 Apr 2026 Shift 1 Paper

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Question : 130 of 150

Marks: +1, -0

\int \frac{x}{x+2} d x

is equal to

$x+2 \log (x+2)+c$
$x+\log (x+2)+c$
$x-\log (x+2)+c$
$x-2 \log (x+2)+c$

Solution:

Concept:

Rewrite the numerator in terms of the denominator to split the fraction into simpler parts.

Explanation:

Write

x

as

(x+2)-2

.

Then

\frac{x}{x+2} = \frac{(x+2)-2}{x+2} = 1 - \frac{2}{x+2}

.

Now integrate term by term:

\int \frac{x}{x+2} dx = \int 1 \, dx - 2\int \frac{1}{x+2} dx

.

This gives

x - 2\ln|x+2| + c

.

Answer:

x - 2 \log (x+2) + c

Option D.

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