A Level

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Evaluate: (i) ∫sin⁡(log⁡x)x dx\int\frac{\sin(\log x)}{x}\,dx (ii) ∫(3sin⁡x+4cos⁡x4sin⁡x−3cos⁡x) dx\int\left(\frac{3\sin x+4\cos x}{4\sin x-3\cos x}\right)\,dx (iii) ∫emtan⁡−1x1+x2 dx\int\frac{e^{m\tan^{-1}x}}{1+x^2}\,dx (iv) ∫xsin⁡(4x2+7) dx\int x\sin(4x^2+7)\,dx

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