- e-x 1-tan x x dx is equal to

The correct option is C none of these ∫ e^ x( x xtan x) = x∫ e^ x ∫ ( xtan x∫ e^ x) ∫ xtan x.e^ x = x.e^ x+∫ ( xtan x.e^ x) ∫ ( xtan x.e^ x) ...

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Byju's Answer

Standard XII

Mathematics

Derivative of Standard Functions

∫ e-x 1-tan x...

Question

$\int e^{- x} (1 - tan x) sec x d x$ is equal to

e^{- x} sec x + c

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e^{- x} tan x + c

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- e^{- x} tan x + c

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none of these

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Solution

The correct option is C none of these
$\int e^{- x} (sec x - sec x tan x)$
$= sec x \int e^{- x} - \int (sec x tan x \int e^{- x}) - \int sec x tan x . e^{- x}$
$= - sec x . e^{- x} + \int (sec x tan x . e^{- x}) - \int (sec x tan x . e^{- x})$
$= - sec x . e^{- x}$

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∫e−x(1−tanx)secxdx is equal to

The correct option is C none of these∫e−x(secx−secxtanx)=secx∫e−x−∫(secxtanx∫e−x)−∫secxtanx.e−x=−secx.e−x+∫(secxtanx.e−x)−∫(secxtanx.e−x)=−secx.e−x

$\int e^{- x} (1 - tan x) sec x d x$ is equal to

The correct option is C none of these
$\int e^{- x} (sec x - sec x tan x)$
$= sec x \int e^{- x} - \int (sec x tan x \int e^{- x}) - \int sec x tan x . e^{- x}$
$= - sec x . e^{- x} + \int (sec x tan x . e^{- x}) - \int (sec x tan x . e^{- x})$
$= - sec x . e^{- x}$