Decompose \(\frac{5}{x(x+5)}\) into partial fractions.

Find \(\int\frac{3x+5}{(x+1)(x+2)}\,dx\).

Find \(\int\frac{1}{x^2-1}\,dx\), for \(x\ne\pm1\).

State the correct partial fraction form for \(\frac{2x+1}{x(x-3)^2}\). Do not solve for the constants.

Find \(\int\frac{4x+1}{x^2+x}\,dx\), for \(x\ne0,-1\).

Decompose \(\frac{x+4}{(x+1)(x-2)}\) into partial fractions.

Find \(\int\frac{x^2+1}{x-1}\,dx\).

Find \(\int\frac{1}{x(x+1)^2}\,dx\), for \(x\ne0,-1\).

Evaluate \(\int_2^3\frac{1}{x^2-x}\,dx\).

Find \(\int\frac{6}{(x-1)(x+2)}\,dx\).