Question

e⁷ˣ+⁴(5x-3)⁸,Integrate the given function defined on proper domain w.r.t. x.

Answer 1

In the attachment I have answered this problem.   The solution is simple and easy to understand.   See the attachment for detailed solution.

Answer 2

we have to find the value $\int{e^{7x}+4(5x-3)^8}\,dx$

we know, int{e^{(ax+b)}}\,dx=e^{(ax+b)}\frac{1}{a}+C[/tex]
and $\int{(ax+b)^n},dx=\frac{(ax+b)^{(n+1)}}{n+1}\frac{1}{a}$

so, $\int{e^{7x}+4(5x-3)^8}\,dx=\int{e^{7x}}\,dx+\int{4(5x-3)^8}\,dx$

$=\frac{1}{7}e^{7x}+\frac{4}{9}(5x-3)^9\frac{1}{5}+C$

$=\frac{e^{7x}}{7}+\frac{4}{45}(5x-3)^9+C$