Differentiate $\mathrm{e}^{\cos 2x}$ with respect to $x$.[1] Find \( \displaystyle\int \mathrm{e

Question

Differentiate $\mathrm{e}^{\cos 2x}$ with respect to $x$.[1] Find $ \displaystyle\int \mathrm{e}^{\cos 2x} \sin 4x \, \mathrm{d}x$.[3] It is given that $2 \cos A \sin B = \sin(A + B) - \sin(A - B)$. By using this result, find $\displaystyle\int \mathrm{e}^{\cos 2x} (\cos 3x \sin x) \, \mathrm{d}x$.[3]

Accepted Answer

(i) $-2\mathrm e^{\cos 2x}\sin 2x$ (ii) $\mathrm e^{\cos 2x}(1-\cos 2x)+C$ (iii) $\mathrm e^{\cos 2x}\left(\frac34-\frac12\cos 2x\right)+C$

Techniques of Integration - Integration by Parts

Techniques of Integration - Integration by Parts

Video Solution:

Solution:

Solution locked