Question

Evaluate:

$\int (e^{a\ln x}+e^{x\ln a}+\sin \alpha )dx$

Answer 1

$\int (e^{a\ln x}+e^{x\ln a}+\sin \alpha )dx$

$=\int e^{a\ln x}dx+\int e^{x\ln a}dx+\int \sin \alpha dx$

$=\int e^{\ln x^a}dx+\int e^{\ln a^x}dx+\int \sin \alpha dx$

$=\int x^{a}dx+\int a^{x}dx+\sin \alpha \int dx$

$=\frac{x^{a+1}}{a+1}+\frac{a^x}{\ln a}+x\sin \alpha +c$