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Integration by Parts

Prove that in...

Question

Prove that integration of sec²x with respect to x is equal to tanx

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\int \frac{cot x - tan x}{cos 4 x + 1} d x

\frac{1}{2} ln | tan 2 x | + C

C

is an integration constant.

\frac{d x}{(s e c x + c o s e c x + t a n x + c o t x)^{2}} = \frac{x}{a} + \frac{\sqrt{2} c o s x + \frac{p}{4}}{b} + \frac{c o s 2 x}{c} + d,

then a+b+c is equal to

\sqrt{\frac{1 - s i n x}{1 + s i n x}} = s e c x - t a n x

\sqrt{\frac{c o s e c x - 1}{c o s e c x + 1}} = \frac{1}{s e c x + t a n x}

Q. Integrate with respect to

x

:

e^{x} ({sec}^{2} x + tan x)

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