- ex-2 2x1-4tan 2xdx is equal to

The correct option is C 2e^x/2 2x+c ∫ e^x/2 sec 2x(1+4 tan 2x)dx ∫ e^x/22(sec2x+4 tan 2x.sec2x)dx It is in the form of ∫ e^x(f(x)+f^1(x))dx ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Derivatives

∫ ex/2 2x1+4t...

Question

$\int e^{x / 2} sec 2 x (1 + 4 tan 2 x) d x$ is equal to

4 e^{x / 2} sec 2 x + c

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2 e^{x / 2} sec 2 x + c

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e^{x / 2} sec 2 x + c

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^{\frac{1}{2} e^{x / 2} sec 2 x + c}

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Solution

The correct option is C $2 e^{x / 2} sec 2 x + c$
$\int e^{x / 2} s e c 2 x (1 + 4 t a n 2 x) d x$
$\int e^{x / 2} 2 (s e c 2 x + 4 t a n 2 x . s e c 2 x) d x$
It is in the form of
$\int e^{x} (f (x) + f^{1} (x)) d x$
$= e^{x} f (x) + c$
$= 2 e^{x / 2} s e c 2 x + c$
$\int e^{x} s e c 2 x = 2 e^{x / 2} s e c 2 x + c$

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∫ex/2sec2x(1+4tan2x)dx is equal to

The correct option is C 2ex/2sec2x+c∫ex/2sec2x(1+4 tan 2x)dx∫ex/22(sec2x+4 tan 2x.sec2x)dxIt is in the form of∫ ex(f(x)+f1(x))dx=exf(x)+c=2ex/2sec2x+c∫ exsec2x=2ex/2sec2x+c

$\int e^{x / 2} sec 2 x (1 + 4 tan 2 x) d x$ is equal to