$\int e^{\frac{1}{2}x}\sin\left(\frac{4}{5}x\right)dx$

$\frac{x^2}{100}-\frac{4a^2}{169}$

$\frac{4x-3}{5}\:+\:\frac{x+1}{2}$

$\int\left(64x-48x^3+12x^5-x^7\right)dx$

$\int\frac{1}{x^4+5x^3}dx$

$\int_0^2\frac{2x+3}{x^2-4x+8}dx$

$\left(\frac{7x}{x^2+x-6}\right)\cdot\left(\frac{x^2-4x+4}{7x^2+x-8}\right)$