Evaluate: `int(2x^2+7x-3)/(x^2(2x+1))\ dx`

Explanation

`I=int frac{(2 x^{2}+7 x-3) d x}{x^{2}(2 x+1)} `

`text { Let } frac{2 x^{2}+7 x-3}{x^{2}(2 x+1)}=frac{A}{x}+frac{B}{x^{2}}+frac{C}{2 x+1} `

`Rightarrow frac{2 x^{2}+7 x-3}{x^{2}(2 x+1)}=frac{A(x)(2 x+1)+B(2 x+1)+C x^{2}}{x^{2}(2 x+1)} `

`Rightarrow 2 x^{2}+7 x-3=A(2 x^{2}+x)+B(2 x+1)+C x^{2} `

`Rightarrow 2 x^{2}+7 x-3=(2 A+C) x^{2}+(A+2 B) x+B`

Equating coefficients of like terms



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