Question

evaluate the following integral
g'(x)=?

Answer 1

\[\int\limits_{0}^{\sqrt{x}} \ln(t+3^t)dt\]

Answer 2

I think something should be the u but i'm not sure what to do. I have tried multiple different u's

Answer 3

You don't actually have to integrate, you have to differentiate it with respect to x.

Answer 4

ok can you show me how please i don't understand what to do thanks

Answer 5

My OS is lagging very badly and giving me headache so am unable to help you at the moment, but am sure someone else would step in for the rescue! ^_^

Answer 6

use second fundamental theorem of calculus.

Answer 7

It goes like ths
\[ F(x) = \int_0^{g(x)} h(t) dt, \; \; \; F'(x) = h(g(x)) g'(x)\]
your \(g(x) = \sqrt x \) and h(t) = ...