Question

Integrate the following functions w.r.t $X:\frac{10x^9+{10}^x.\log 10}{{10}^x+{10}^{10}}$

Answer 1

Let $I=\int \frac{10x^9+{10}^x.\log 10}{{10}^x+{10}^{10}}.dx$

Put ${10}^x+x^{10}=t$

$\therefore ({10}^x.\log 10+10x^9).dx=dt$

$\therefore I=\int \frac{1}{t}dt=\log |t|+c$

$=\log |{10}^x+x^{10}|+c$