The value of integral ∫ e x [ 1 + t a n x 2 t a n x + cot 2 ( x + 4 π ) ] dx is equal to -

∫ e x [ 1 + t a n x 2 t a n x + cosec 2 ( x + 4 π ) ] dx ∫ e x [ cot ( x + 4 π ) + cosec 2 ( x + 4 π ) ] d x e x cot ( x + 4 π ) + C = e x tan ( x − 4 π ) + C

Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationMiscellaneous formMedium2 minQB

MathematicsMediumsingle choice

The value of integral $\int e^{x} [\frac{2 t a n x}{1 + t a n x} + cot^{2} (x + \frac{π}{4})] dx$ is equal to -

Options:

Answer:

Solution:

$\int e^{x} [\frac{2 t a n x}{1 + t a n x} + cosec^{2} (x + \frac{π}{4})] dx$

$\int e^{x} [cot (x + \frac{π}{4}) + cosec^{2} (x + \frac{π}{4})] d x$

$e^{x} cot (x + \frac{π}{4}) + C = e^{x} tan (x - \frac{π}{4}) + C$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Miscellaneous form

⏱ 2mℹ️ Source: QB

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