Question

$\int \left(e^{a\ln x}+e^{x\ln a}\right)dx$, where $x>0,a>0$

Answer 1

$\int \left(e^{a\ln x}+e^{x\ln a}\right)dx;x>0,a>0$

$\therefore e^{\ln }f\left(x\right)=f\left(x\right)$

$\therefore \int \left(e^{a\ln x}+e^{x\ln a}\right)dx$

$\int \left(e^{\ln \left(x^a\right)}\right)+e^{\ln \left(a^x\right)}dx$

$\int \left(x^a+a^x\right)dx$

$\int x^{2}dx+\int a^{x}dx$

$\frac{x^{a+1}}{a+1}+\frac{a^x}{\ln \left(a\right)}+c$