∫（x^5+5^x)dx;∫x2^x²dxevaluate the integral. Thank you.
Welcome and Thanks for requesting me.
I am working on your question and will post the answer shortly.
(1) ∫ (x^5 + 5^x)dx
= ∫ x^5 dx + ∫ 5^x dx
= (1/6)(x^6) + (1/ln 5)(5^x) + C
(2) Let x^2 = u then 2x dx = du
x dx = du/2
∫ x 2^(x^2) dx = ∫ (2^u)(du/2)
= (1/2)(2^u)(1/ln 2) + C
= (1/ln 4)(2^(x^2)) + C
I hope that helps. Let me know if you need any clarifications on my answers. I will be happy to provide them. Else, please give a rating for my answer.
I have a Master's degree in Engineering and a very wide teaching experience of more than 25 years at various levels.