ज्ञात करें `int ((x^2 +1)e^x)/((x+1)^2)dx`

Explanation

`int ((x^2+1)e^x)/((x+1)^2)dx=inte^x ((x^2-1)+2)/((x+1)^2)dx`
`=int e^x[x^2/((x+1)^2)+2/((x+1)^2)]dx = int e^x[(x-1)/(x+1)+2/((x+1)^2)]dx`
`=int e^x[f(x) +f'(x)]dx,` जहां `f(x)=(x-1)/(x+1)`
`=e^(x)f(x)+c =e^x ((x-1)/(x+1))+c`
second method : `x^2 +1 (x+1)^(2)-2x` लिखकर आगे बढ़ें |