UV আকারের (Integration by parts)
∫x3exdx=f(x)+c \int x^{3} e^{x} dx = f{\left ( x \right )} + c ∫x3exdx=f(x)+c হয় তবে f(x)=?
∫xneaxdx \int \mathrm{x}^{\mathrm{n}} \mathrm{e}^{\mathrm{ax}} \mathrm{dx} ∫xneaxdx
=eax[xna−nxxn−1a2+n(n−1)xn−2a3−n(n−1)(n−2)xn−3a4+..]+c∴∫x3exdx=ex[x3−3x2+6x−6]+c \begin{array}{l} =\mathrm{e}^{\mathrm{ax}}\left[\frac{\mathrm{x}^{\mathrm{n}}}{\mathrm{a}}-\frac{\mathrm{nx} \mathrm{x}^{n-1}}{\mathrm{a}^{2}}+\frac{\mathrm{n}(\mathrm{n}-1) \mathrm{x}^{\mathrm{n}-2}}{\mathrm{a}^{3}}-\frac{\mathrm{n}(\mathrm{n}-1)(\mathrm{n}-2) \mathrm{x}^{n-3}}{\mathrm{a}^{4}}+. .\right]+c \\ \therefore \int \mathrm{x}^{3} \mathrm{e}^{\mathrm{x}} \mathrm{dx}=\mathrm{e}^{\mathrm{x}}\left[\mathrm{x}^{3}-3 \mathrm{x}^{2}+6 \mathrm{x}-6\right]+c \end{array} =eax[axn−a2nxxn−1+a3n(n−1)xn−2−a4n(n−1)(n−2)xn−3+..]+c∴∫x3exdx=ex[x3−3x2+6x−6]+c
∫f(x)dx=x+e2x \int f{\left ( x \right )} dx = x + e^{2 x} ∫f(x)dx=x+e2x হলে f(x)=?
f(x)=x2 \mathrm{f(x)=x^{2}} f(x)=x2
∫xx(1+logx)dx=? \int x^{x} \left ( 1 + \log{x} \right ) dx = ? ∫xx(1+logx)dx=?
f(x)=sinx+cosx, g(x)=lnx
∫x2{g(x)}2dx \int x^{2} \left \lbrace g{\left ( x \right )} \right \rbrace^{2} dx ∫x2{g(x)}2dx এর মান নিচের কোনটি ?
