$Q1)\int \frac{10x^{9}+10^{x}ln10}{10^{x}+x^{10}}dx$
$=ln\left | 10^{x}+x^{10} \right |+c$
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$Q4)\int (e^{xlna}+e^{alnx}+e^{alna})dx$
$\int (e^{lna^{x}}+e^{lnx^{a}}+e^{lna^{a}})dx$
$\int ({a^{x}}+{x^{a}}+a^{a})dx$
$=\frac{a^{x}}{lna}+\frac{x^{a+1}}{a+1}+a^{a}x+c$
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$Q5)\int \frac{(a^{x}+b^{x})^{2}}{a^{x}b^{x}}dx$
$=\int \frac{a^{2x}+2a^{x}b^{x}+b^{2x}}{a^{x}b^{x}}dx$
$=\int[(\frac{a}{b})^{x}+2+(\frac{b}{a})^{x}]dx$
$=\frac{(\frac{a}{b})^{x}}{ln\frac{a}{b}}+2x+\frac {(\frac{b}{a})^{x}}{ln\frac{b}{a}}+c$
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$Q7)\int e^{xln2017}e^{x}dx$
$\int e^{ln2017^{x}}e^{x}dx$
$\int 2017^{x}e^{x}dx=\int (2017e)^{x}dx$
$=\frac{(2017e)^{x}}{ln(2017e)}+c$
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