The integral ∫ 2 x 3 - 1 x 4 + x d x , is equal to

I = ∫ 2 x 3 - 1 x 4 + x d x ⇒ I = ∫ 2 x - 1 x 2 x 2 + 1 x d x Put, x 2 + 1 x = t ⇒ 2 x - 1 x 2 d x = d t ∴ I = ∫ d t t = l o g e t + C = l o g e x 2 + 1 x + C = l o g e x 3 + 1 x + C

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 minPYQ_2019

MathematicsMediumsingle choice

The integral $\int \frac{2 x^{3} - 1}{x^{4} + x} d x$ , is equal to

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Solution:

$I = \int \frac{2 x^{3} - 1}{x^{4} + x} d x$
$\Rightarrow I = \int \frac{2 x - \frac{1}{x^{2}}}{x^{2} + \frac{1}{x}} d x$
Put, $x^{2} + \frac{1}{x} = t$ $\Rightarrow (2 x - \frac{1}{x^{2}}) d x = d t$
$∴ I = \int \frac{d t}{t} = l o g_{e} (t) + C$
$= l o g_{e} (x^{2} + \frac{1}{x}) + C$
$= l o g_{e} |\frac{(x^{3} + 1)}{x}| + C$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2019

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