- e2 x- 2 x- 2 x -tan 2 x- d xA- e2 x- 2 x-CB- e2 x- 2 x-2- C- e2 x- 2 x tan 2 x-2- CD- cannot be determined

The correct option is B + C We can clearly see that the given question is of type ∫ e^kx [f(kx) + f'(kx)]dx where k = 2 ∫ e^2x [sec 2x + sec 2x.tan 2x]dx wher ...

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Byju's Answer

Standard XII

Physics

Definite Integrals

∫ e2 x[ 2 x+ ...

Question

$\int e^{2 x}$ [sec 2x + sec 2x.tan 2x]dx

.sec 2x + C

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+ C

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+ C

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Solution

The correct option is B
+ C

We can clearly see that the given question is of type $\int e^{k x}$ [f(kx) + f'(kx)]dx

where k = 2

$\int e^{2 x}$ [sec 2x + sec 2x.tan 2x]dx

where f(kx) = sec 2x

and f'(kx) = sec 2x.tan 2x

Hence the answer for this will be $\frac{1}{k} e^{k x}$ f(kx) + C

$\frac{e^{2 x} . s e c 2 x}{2}$ + C

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Similar questions

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∫e2x [sec 2x + sec 2x.tan 2x]dx

The correct option is B + C We can clearly see that the given question is of type ∫ekx [f(kx) + f'(kx)]dx where k = 2 ∫e2x [sec 2x + sec 2x.tan 2x]dx where f(kx) = sec 2x and f'(kx) = sec 2x.tan 2x Hence the answer for this will be 1kekx f(kx) + C e2x.sec2x2 + C

$\int e^{2 x}$ [sec 2x + sec 2x.tan 2x]dx