Blog

Pattern – 5 : Indefinite Integration

No Comments

⋆ Pattern – 5

$\int\frac{f\prime\left(x\right)}{f\left(x\right)}\ dx=\log{\left|f\left(x\right)\right|}+c$

$1)\ \int\frac{x^{e-1}+e^{x-1}}{x^e+e^x}$

$=\frac{1}{e}\ \ \int\frac{ex^{e-1}+e\times e^{x-1}}{x^e+e^x}\ dx$

$=\frac{1}{e}\ \ \int\frac{ex^{e-1}+e^x}{x^e+e^x}\ dx$

$=\frac{1}{e}\log{\left|x^e+e^x\right|}\ dx$