Trigonometric Antiderivatives
Trigonometric Antiderivatives
IB Year 6 | Grade 12
TGM Original
Reverse the standard derivative formulas. For tangent and cotangent, rewrite in sine and cosine and apply the logarithmic reverse-chain-rule form.
| Integrand | Antiderivative |
|---|---|
| \(\sin x\) | \(-\cos x+C\) |
| \(\cos x\) | \(\sin x+C\) |
| \(\sec^2x\) | \(\tan x+C\) |
| \(\operatorname{cosec}^2x\) | \(-\cot x+C\) |
| \(\sec x\tan x\) | \(\sec x+C\) |
| \(\operatorname{cosec}\,x\cot x\) | \(-\operatorname{cosec}\,x+C\) |
| \(\tan x\) | \(-\ln|\cos x|+C\) |
| \(\cot x\) | \(\ln|\sin x|+C\) |
For an angle \(ax+b\), divide the corresponding antiderivative by \(a\), where \(a\ne0\). Work on an interval without a zero denominator.
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