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These are the Transum resources related to the statement: "Carry out simple cases of integration by substitution and integration by parts; understand these methods as the inverse processes of the chain and product rules respectively (Integration by substitution includes finding a suitable substitution and is limited to cases where one substitution will lead to a function which can be integrated; integration by parts includes more than one application of the method but excludes reduction formulae)".

Here are some exam-style questions on this statement:

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*The acceleration, \(a\) ms*" ... more^{-2}, of an object at time \(t\) seconds is given by - "
*Given that \( \frac{dy}{dx} = \sin(x + \frac{\pi}{3})\) and \(y = 5\) when \(x = \frac{8\pi}{3}\), find \(y\) in terms of \(x\).*" ... more - "
*(a) Using a suitable substitution, or otherwise, find*" ... more - "
*Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \).*" ... more - "
*Find \(f(x)\) if:*" ... more

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