Vi bruker substitusjonen

$$u = \sin(x) \implies \frac{\mathrm{d}u}{\mathrm{d}x} = \cos(x) \implies \mathrm{d}u = \cos(x)\,\mathrm{d}x$$

Integralet skrives om:

$$\int \sin^3(x) \cdot \cos(x)\,\mathrm{d}x = \int u^3\,\mathrm{d}u$$

Vi integrerer:

$$\int u^3\,\mathrm{d}u = \frac{u^4}{4} + C$$

Vi substituerer tilbake $u = \sin(x)$:

$$\frac{u^4}{4} + C = \mathbf{\underline{\underline{\dfrac{\sin^4(x)}{4} + C}}}$$