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\begin{align*} \int \frac 1 {\sin x +3\cos x}\ dx &= \int \frac 1 {2\sin \frac x 2\cos \frac x 2 +3\cos^2 \frac x 2 - 3 \sin^2 \frac x 2}\ dx \\ &= \int \frac 1 ... |
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How to evaluate the trigonometric integral $\int \frac{1}{\cos x+\tan x...
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Integrate both sides to get $\displaystyle f(x)g(x)=\int\! f(x)g'(x)\, dx +\int\! f'(x)g(x)\, dx$. ... . Finally, \[\int e^x\cos x\, dx =\frac{1}{2}e^x\sin x+\frac{1}{2}e^x\cos x +C.\] ... |
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