The value of ∫ [ ( x − 1 ) 3 ( x + 2 ) 5 ] 4 1 1 d x , is

I = ∫ ( x + 2 x − 1 ) 3/4 ( x + 2 ) 2 1 d x Let x + 2 x − 1 = t ⇒ ( x + 2 ) 2 3 d x = d t ⇒ I = 3 1 ∫ t 3/4 1 d t = 3 1 ( 1/4 t 1/4 ) + C = 3 4 t 1/4 + C = 3 4 ( x + 2 x − 1 ) 1/4 + C

Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationMiscellaneous formMedium2 minPYQ_2022

MathematicsMediumsingle choice

The value of $\int \frac{1}{[ ( x - 1 ) ^{3} ( x + 2 ) ^{5} ] ^{\frac{1}{4}}} d x$ , is

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Solution:

$I = \int \frac{1}{( \frac{x - 1}{x + 2} ) ^{3/4} ( x + 2 ) ^{2}} d x$ Let $\frac{x - 1}{x + 2} = t \Rightarrow \frac{3 d x}{( x + 2 ) ^{2}} = d t$ $\Rightarrow I = \frac{1}{3} \int \frac{1}{t ^{3/4}} d t = \frac{1}{3} (\frac{t ^{1/4}}{1/4}) + C = \frac{4}{3} t^{1/4} + C = \frac{4}{3} (\frac{x - 1}{x + 2})^{1/4} + C$

Stream:BITSATSubject:MathematicsTopic:Indefinite IntegrationSubtopic:Miscellaneous form

⏱ 2mℹ️ Source: PYQ_2022

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