Integrales útiles al trabajar con Series de Fourier

$$\int x \: sin \: axdx = \frac{1}{a^2} sin \: ax- \frac{x}{a} cos \: ax+C$$

$$\int x \: cos \: axdx = \frac{1}{a^2} cos \: ax- \frac{x}{a} sin \: ax+C$$

$$\int x^2 \: sin \: axdx = \left( \frac{2}{a^3} - \frac{x^2}{a} \right) cos \: ax- \frac{2x}{a^2} sin \: ax+C$$

$$\int x^2 \: cos \: axdx = \left( \frac{x^2}{a} - \frac{2}{a^3} \right) sin \: ax- \frac{2x}{a^2} cos \: ax+C$$

$$\int x^3 \: sin \: axdx = \left( \frac{6x}{a^3} - \frac{x^3}{a} \right) cos \: ax+ \left(\frac{3x^2}{a^2} - \frac{6}{a^4} \right) sen \: ax+C$$

$$\int x^3 \: cos \: axdx = \left( \frac{x^3}{a} - \frac{6x}{a^3} \right) sin \: ax+ \left(\frac{3x^2}{a^2} - \frac{6}{a^4} \right) cos \: ax+C$$

$$\int x^4 \: sin \: axdx = \left( \frac{4x^3}{a^2} - \frac{24x}{a^4} \right) sin \: ax- \left(\frac{x^4}{a} - \frac{12x^2}{a^3} + \frac{24}{a^5} \right) cos \: ax+C$$

$$\int x^4 \: cos \: axdx = \left( \frac{4x^3}{a^2} - \frac{24x}{a^4} \right) cos \: ax+ \left(\frac{x^4}{a} - \frac{12x^2}{a^3} + \frac{24}{a^5} \right) sin \: ax+C$$