Using Trigonometric Identities
\(\DeclareMathOperator{cosec}{cosec}\)
Example
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\[\int \sin3x\cos3x \, dx \]
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\[\int \frac{1}{2}\sin6x \, dx \]
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\[\frac{1}{2}\times-\frac{1}{6}\cos6x+c\]
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\[-\frac{1}{12}\cos6x+c\]
Example
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\[\int (\sec x+\tan x)^2 \, dx \]
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\[\int (\sec^2x+2\sec x\tan x+\tan^2x) \, dx \]
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\[\int (\sec^2x+2\sec x\tan x+sec^2x-1) \, dx \]
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\[\int (2\sec^2x+2\sec x\tan x-1) \, dx \]
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\[2\tan x+2\sec x-x+c\]
\(\int \cot^2x \, dx\)
- \(\int (\cosec^2x-1) \, dx\)
- \(-\cot x-x+c\)
\(\int \cos^2x \, dx\)
- \(\int \frac{\cos2x+1}{2} \, dx\)
- \(\int \left( \frac{1}{2}\cos2x+\frac{1}{2} \right) \, dx\)
- \(\frac{1}{4}\sin2x+\frac{1}{2}x +c\)