Solveeit Logo
Login

Question

Mathematics Question on integral

Integrate the function: e5log x−e4 logxe3 logx−e2 logx\frac{e^{5log\,x-e^{4\,logx}}}{e^{3\,logx}-e^{2\,logx}}

Answer

e5log x−e4 logxe3 logx−e2 logx\frac{e^{5log\,x-e^{4\,logx}}}{e^{3\,logx}-e^{2\,logx}}=e4 logx(elog x−1)e2 logx(elogx−1)\frac{e^{4\,logx(e^{log\,x-1})}}{e^{2\,logx}(e^{logx-1})}

=e2 logxe^2\,logx

=elog x2e^{log\,x^2}

=x2

∴∫\frac{e^{5log\,x-e^{4\,logx}}}{e^{3\,logx}-e^{2\,logx}}$$=\int x^2dx=\frac{x^3}{3}+C