- esin x x cos3 x - sin x-cos2 xdx-is equal to

We have ∫ e^sin x (x cos^3 x sin x/cos^2 x)dx = ∫ xe^sin x cos xdx ∫ e^sin x (secx tan x)dx = [xe^sin x ∫ e^sin x dx] [e^sin x sec x ∫ e^sin xdx] = ...

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Byju's Answer

Standard XIII

Mathematics

Integration by Parts

∫ esin x x co...

Question

$\int e^{s i n x} (\frac{x c o s^{3} x - s i n x}{c o s^{2} x}) d x$ ,is equal to

e^{s i n x} (t a n x + x) + C

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e^{s i n x} (x - s e c x) + C

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e^{s i n x} (s e c x + t a n x) + C

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Solution

The correct option is B $e^{s i n x} (x - s e c x) + C$
We have
$\int e^{s i n x} (\frac{x c o s^{3} x - s i n x}{c o s^{2} x}) d x = \int x e^{s i n x} c o s x d x - \int e^{s i n x} (s e c x t a n x) d x = [x e^{s i n x} - \int e^{s i n x} d x] - [e^{s i n x} s e c x - \int e^{s i n x} d x] = e^{s i n x} (x - s e c x) + C$

Suggest Corrections

∫esinx(x cos3x−sinxcos2x)dx,is equal to

The correct option is B esinx(x−secx)+CWe have ∫esinx(x cos3x−sinxcos2x)dx=∫xesinxcos xdx−∫esinx(secx tanx)dx=[xesinx−∫esinxdx]−[esinxsec x−∫esinxdx]=esinx(x−secx)+C

$\int e^{s i n x} (\frac{x c o s^{3} x - s i n x}{c o s^{2} x}) d x$ ,is equal to