Compute the integral:

Calculus Level pending

∫ x 2 x ( 2 + 2 ln ⁡ x ) d x = ? \int x^{2x} (2+2\ln x) \ dx = \ ?

Notation: C C in the answer options denotes the constant of integration.

x 4 x { x }^{ 4x } x 2 x + C { x }^{ 2x } +C x x + C { x }^{ x } + C

Pranesh Pyara Shrestha by Pranesh Pyara Shrestha , 18, Nepal

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

I = ∫ x 2 x ( 2 + 2 ln ⁡ x ) d x = ∫ d d x ( x 2 x ) d x = x 2 x + C I = \int x^{2x}(2+2\ln x) \ dx = \int \frac d{dx} \left(x^{2x}\right) dx = \boxed{x^{2x} + C}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ron Gallagher
Jul 3, 2020

x^(2x) = exp(2x lnx). Now, make the substitution u = 2x lnx. Then, du = (2 ln(x) + 2) dx. The integrand then becomes exp(u) du, so that the integral is exp(2x lnx) + constant, or x^(2x) + constant.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...