The correct option is A e^xx+c Let x x =t On differentiating, we get x(1+xtanx)dx=dt Substituting these results in ∫ e^x x· nbsp;x(1+xtanx) ...

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Standard XII

Mathematics

Special Integrals - 1

∫ exx·x1+xtan...

Question

$\int e^{x sec x} \cdot sec x (1 + x tan x) d x =$

e^{x sec x} + c

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- e^{x sec x} + c

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

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- e^{x tan x} + c

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Solution

The correct option is A $e^{x sec x} + c$
Let $x sec x = t$
On differentiating, we get
$sec x (1 + x tan x) d x = d t$
Substituting these results in
$\int e^{x sec x} \cdot sec x (1 + x tan x) d x$
$= \int e^{t} d t = e^{t} + c$
$= e^{x sec x} + c$

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∫exsecx⋅secx(1+xtanx)dx=

The correct option is A exsecx+cLet xsecx=tOn differentiating, we getsecx(1+xtanx)dx=dtSubstituting these results in∫exsecx⋅secx(1+xtanx)dx=∫etdt=et+c=exsecx+c

$\int e^{x sec x} \cdot sec x (1 + x tan x) d x =$

The correct option is A $e^{x sec x} + c$
Let $x sec x = t$
On differentiating, we get
$sec x (1 + x tan x) d x = d t$
Substituting these results in
$\int e^{x sec x} \cdot sec x (1 + x tan x) d x$
$= \int e^{t} d t = e^{t} + c$
$= e^{x sec x} + c$