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Určete integrál:

$$\int \cos (\log x) dx$$

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Zavedeme substituci:
$$\align \log x &= z\\ {dx \over x}&=dz \\ dx&={x dz}\\ x&=e^z\\ dx&=e^z dz\endalign$$

$$\int \cos (\log x) dx = \int \cos z e^z dz = {e^z \over 2}(\sin z +\cos z) = {x \over 2} [\sin(\log x) + \cos (\log x)]$$

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