Find the integral -x-1x2-2x-4dx

Given, f(x)=x+1x^2+2x 4 So, to integrate the given function we use substitution method. Let t=x^2+2x 4 ⇒ dtdx=2x+2=2(x+1) Or, dt2=(x+1)dx Thus, substituting thi ...

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Standard XI

Physics

Antiderivative

Find the inte...

Question

Find the integral $\int \frac{x + 1}{x^{2} + 2 x - 4} d x$

ln (x^{2} + 2 x - 4) + C

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\frac{1}{2} ln (x^{2} + 2 x) + C

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\frac{1}{2} ln (x^{2} + 2 x - 4) + C

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\frac{1}{2} ln (x + 1) + C

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Solution

The correct option is C $\frac{1}{2} ln (x^{2} + 2 x - 4) + C$
Given, $f (x) = \frac{x + 1}{x^{2} + 2 x - 4}$
So, to integrate the given function we use substitution method.
Let $t = x^{2} + 2 x - 4 \Rightarrow \frac{d t}{d x} = 2 x + 2 = 2 (x + 1)$
Or, $\frac{d t}{2} = (x + 1) d x$
Thus, substituting this value in the given function we have,
$\int \frac{x + 1}{x^{2} + 2 x - 4} d x = \int \frac{1}{2 t} d t = \frac{1}{2} ln t + C$
$\Rightarrow \frac{1}{2} ln (x^{2} + 2 x - 4) + C$

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