int (dx)/(1+3sin^2x+8 cos^2x)...

`int (dx)/(1+3sin^2x+8 cos^2x)`

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MODERN PUBLICATION-INTEGRALS-EXERCISE (7d) LONG ANSWER TYPE QUESTION (I)

int(secx- tan x)/(sec x+ tan x) dx
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(i) int 1/(4sin^2x+5cos^2x) dx (ii) int (dx)/(cos^2 x+2 sin^2x)
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int(dx)/(1+3sin^2x).
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int (dx)/(1+3sin^2x+8 cos^2x)
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int sqrt[[1-x]/[1+x]]dx
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(i) int sqrt((a+x)/(a-x)) dx (ii) int sqrt((a-x)/(a+x)) dx
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int((sinx+cosx))/(sqrt(sin2x))dx
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Prove that: int (dx)/(xsqrt(x^2-a^2))=1/a sec^-1 (x/a)+c
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