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Určete integrál:

$$\int e^x \sqrt{1+e^x} dx$$

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Zavedeme substituci:
$$\align 1+e^x&=z \\ e^x\ dx&=dz \endalign$$

$$\int e^x \sqrt{1+e^x} dx = \int z^{1 \over 2} dz = {2 \over 3} z^{3 \over 2} = {2 \over 3} \sqrt{(1+e^x)^3}$$


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