Basic integration by parts

A question is this type if and only if it asks to find or evaluate a single definite or indefinite integral using integration by parts once, with standard functions like x·e^(ax), x·sin(ax), x·cos(ax), or x·ln(x).

27 questions · Moderate -0.2

1.08i Integration by parts

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AQA Paper 3 2021 June Q8

6 marks Standard +0.3

Given that $$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} x \cos x \, dx = a\pi + b$$ find the exact value of \(a\) and the exact value of \(b\). Fully justify your answer. [6 marks]

Pre-U Pre-U 9794/2 2011 June Q3

5 marks Moderate -0.8

Use integration by parts to find \(\int x \sin 3x \, dx\). [5]