Question

Integration of e^xloga+e^alogx+e^aloga

Answer 1

This is a very easy integration...and the solution of the problem is given below..

Answer 2

we have to find $\int{e^{xloga}+e^{alogx}+e^{aloga}}\,dx$

or, $\int{a^x+x^a+a^a}\,dx$


we know, $\int{a^x}\,dx=\left[\frac{a^x}{lna}\right]+C$

$\int{x^n}=\left[\frac{x^{n+1}}{n+1}\right]+C$

so,
$\int{a^x+x^a+a^a}\,dx\\\\\\=\int{a^x}\,dx+\int{x^a}\,dx+\int{a^a}\,dx\\\\\\=\left[\frac{a^x}{lna}\right]+\left[\frac{x^{a+1}}{a+1}\right]+a^ax+C$