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Antiderivatives — Notes & Practice
Antiderivatives
تمارين شاملة على اللوغاريتمات، التكاملات الأسية، الدوال المثلثية، ومتطابقات الزوايا.
Practice logarithmic integrals, exponential chain rule, inverse trig, double-angle identities, and power-reducing identities in one polished lesson page.
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مسائل الدرس — الدوال الأصلية
Antiderivatives — Notes & Practice
Question 1 / 15
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💡 Tips
⭐ Golden Rule
Prepare first, then integrate: simplify, match derivatives, convert trig forms, and use identities before solving.
Quick formulas
\(\int \frac{u'(x)}{u(x)}dx=\ln|u(x)|+C\)
\(\int e^{ax+b}dx=\frac1a e^{ax+b}+C\)
\(\int \cot x\,dx=\ln|\sin x|+C\)
\(\int \tan x\,dx=-\ln|\cos x|+C\)
\(\cos^2x-\sin^2x=\cos 2x\)
\(\sin^2x=\frac12(1-\cos2x)\)
\(\cos^23x=\frac12(1+\cos6x)\)
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