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- Each integrand becomes a basic form after a rewrite (cancel a factor or use an identity).\displaystyle\int \dfrac{\sin 2x}{\cos x}\,dx\displaystyle\int \dfrac{\cos 2x}{\cos x - \sin x}\,dx\displaystyle\int \dfrac{e^{2x} - 1}{e^x - 1}\,dx
- Find dx1 + e^x by two routes.
- Find dxx(5 + √(x)) for x > 0.
- Each integral needs a substitution first and then integration by parts.
- Both integrals contain √(x² + 4).
- The function e^xx has no elementary antiderivative.
- Take $g
- Let $F
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Choosing an integration technique: the lesson ›More Chapter 1 worksheets: Integration techniques
- 1.1Integration by parts
- 1.2Trigonometric integrals
- 1.3Trigonometric substitution
- 1.4Integration by partial fractions
- 1.5Choosing an integration technique