3.1 Integration by parts  (Page 3/5)

${\displaystyle \int x^3{e}^{2x}dx}$

${\displaystyle \int x^3\text{ln}(x)dx}$

${\displaystyle \int y^3\text{cos}ydx}$

${\displaystyle \int x^2\text{arctan}xdx}$

${\displaystyle \int e^{3x}\text{sin}(2x)dx}$

${\displaystyle \int v\text{sin}vdv}$

${\displaystyle \int \text{ln}xdx}$ ( Hint: ${\displaystyle \int \text{ln}xdx}$ is equivalent to ${\displaystyle \int 1·\text{ln}(x)dx}.)$

${\displaystyle \int x\text{cos}xdx}$

${\displaystyle \int {\text{tan}}^{\mathrm{-1}}xdx}$

${\displaystyle \int x^2}{e}^{x}dx$

${\displaystyle \int x\text{sin}(2x)dx}$

${\displaystyle \int x{e}^{4x}dx}$

${\displaystyle \int x{e}^{\text{−}x}dx}$

${\displaystyle \int x\text{cos}3xdx}$

${\displaystyle \int x^2}\text{cos}xdx$

${\displaystyle \int x\text{ln}xdx}$

${\displaystyle \int \text{ln}(2x+1)dx}$

${\displaystyle \int x^2{e}^{4x}}dx$

${\displaystyle \int e^x\text{sin}xdx}$

${\displaystyle \int e^x\text{cos}xdx}$

${\displaystyle \int x{e}^{\text{−}{x}^2}dx}$

${\displaystyle \int x^2{e}^{\text{−}x}dx}$

${\displaystyle \int \text{sin}(\text{ln}(2x))dx}$