u-Substitution Method (Cancelling Method) Examples
u-Substitution Method (Cancelling Method) Examples
- Find \(\displaystyle\displaystyle \displaystyle\int x \sin(3x^{2} + 1)\) \(\mathrm{d}x\).
- Find \(\displaystyle\displaystyle \displaystyle\int e^{2x} \sqrt{e^{2x} + 1}\) \(\mathrm{d}x\).
- Find \(\displaystyle\displaystyle \displaystyle\int \sec^{2}x \sqrt{\tan x + 8}\) \(\mathrm{d}x\).
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Answer:(i) \(-\displaystyle\frac{1}{6} \cos(3x^2+1) + C\); (ii) \(\displaystyle\frac{1}{3} (e^{2x}+1)^{\frac{3}{2}} + C\); (iii) \(\displaystyle\frac{2}{3} (\tan x + 8)^{\frac{3}{2}} + C\)
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