Practice section 2 of 10

Integrate with respect to $x$: (a) $e^{3x}-e^{-x}$; (b) $xe^{x^2}$; (c) $e^{\tan x}\sec^2x$.

Integrate with respect to $x$: (a) $\frac1{\sqrt{4-x^2}}$; (b) $\frac1{9+x^2}$; (c) $\frac1{\sqrt{1-4x^2}}$. For (c), compare the MF27 formula with the general composite formula.

Integrate with respect to $x$: (a) $\frac1{10+x^2}$; (b) $\frac1{\sqrt{2-x^2}}$.

Find (a) $\int\frac1{t^2+4t+13}\,dt$; (b) $\int\frac1{2x^2+8x+9}\,dx$; (c) $\int\frac1{\sqrt{13+8x-4x^2}}\,dx$.

Integrate with respect to $x$: (a) $1/(x^2-4)$; (b) $1/(4x^2-1)$; (c) $1/(16-4x^2)$.

Integrate with respect to $x$: (a) $1/(x^2-1)$; (b) $1/(16-x^2)$.