The value of - 3 x d x will be

The correct option is A 1/2[sec x tan x+log(sec x+tan x)]Let I=∫ sec^3 x dx = ∫ sec x sec^2 x dx ⇒ I = sec x tan x ∫ sec x tan^2 x dx ⇒ I= sec x tan x ∫ ...

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Byju's Answer

Standard XII

Mathematics

Integration by Partial Fractions

The value of ...

Question

The value of $\int s e c^{3} x d x$ will be

\frac{1}{2} [s e c x t a n x + l o g (s e c x + t a n x)]

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\frac{1}{3} [s e c x t a n x + l o g (s e c x + t a n x)]

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\frac{1}{4} [s e c x t a n x + l o g (s e c x + t a n x)]

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\frac{1}{8} [s e c x t a n x + l o g (s e c x + t a n x)]

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Solution

The correct option is A $\frac{1}{2} [s e c x t a n x + l o g (s e c x + t a n x)]$
Let $I = \int s e c^{3} x d x = \int s e c x s e c^{2} x d x$
$\Rightarrow I = s e c x t a n x - \int s e c x t a n^{2} x d x \Rightarrow I = s e c x t a n x - \int s e c x (s e c^{2} x - 1) d x \Rightarrow I = s e c x t a n x - \int s e c^{3} x d x + \int s e c x d x \Rightarrow I = s e c x t a n x - I + l o g (s e c x + t a n x) \Rightarrow 2 I = s e c x t a n x + l o g (s e c x + t a n x) \Rightarrow I = \frac{1}{2} [s e c x t a n x + l o g (s e c x + t a n x)]$

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The value of ∫sec3x dx will be

The value of $\int s e c^{3} x d x$ will be