UV আকারের (Integration by parts)
∫xlogxdx=?\int x \log x dx = ? ∫xlogxdx=?
1+x+c
12x2logx−14x2+c\frac{1}{2}x² logx - \frac{1}{4}x² + c21x2logx−41x2+c
0+C
1+logx+C1+logx+C1+logx+C
∫xlogxdx \int x \log x d x ∫xlogxdx
Integrating by parts
⇒logx∫xdx−∫(d(logxdx)(∫xdx)dx=log=x22logx−x24+C \begin{array}{l} \Rightarrow \log x \int x d x-\int\left(\frac{d(\log x}{d x}\right)\left(\int x d x\right) d x=\log \\ =\frac{x^{2}}{2} \log x-\frac{x^{2}}{4}+C \end{array} ⇒logx∫xdx−∫(dxd(logx)(∫xdx)dx=log=2x2logx−4x2+C
∫e2xcosexdx=?\int e^{2 x} \cos e^{x} d x = ?∫e2xcosexdx=?
∫x3sinxdx=?\int x^{3} \sin x d x = ?∫x3sinxdx=?
∫ln(1+x)1+xdx equals\displaystyle\int {\dfrac{{\ln \left( {1 + {x}} \right)}}{{1 + {x}}}} dx\,equals∫1+xln(1+x)dxequals
∫x3exdx=f(x)+c \int x^{3} e^{x} dx = f{\left ( x \right )} + c ∫x3exdx=f(x)+c হয় তবে f(x)=?
