∫ c o s x + 3 s i n x d x equals

∫ c o s x + 3 s i n x d x = 2 1 ∫ sec ( x − 3 π ) d x = 2 1 lo g tan ( 2 x − 6 π + 4 π ) + c = 2 1 lo g tan ( 2 x + 12 π ) + c .

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 minPYQ_2007

MathematicsMediumsingle choice

$\int \frac{d x}{c o s x + 3 s i n x}$ equals

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Answer:

Solution:

$\int \frac{d x}{c o s x + 3 s i n x}$ $= \frac{1}{2} \int sec (x - \frac{π}{3}) d x$ $= \frac{1}{2} lo g tan (\frac{x}{2} - \frac{π}{6} + \frac{π}{4}) + c$ $= \frac{1}{2} lo g tan (\frac{x}{2} + \frac{π}{12}) + c$ .

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2007

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