Integrate the following functions w.r.t. $x$

$\sqrt{5x^2+3}$

Integrate the following functions w.r.t. $x$

$x^2·\sqrt{a^2-x^6}$

Integrate the following function with respect to $x$:

$\sqrt{(6-x)(x-4)}$

Evaluate the integral:$\int \frac{(x+1)e^{x}dx}{{\cos }^2\left(x{e}^x\right)}$

Evaluate the integral:$\int (1-x)\sqrt{1+x}dx$

Integrate the following functions w.r. to $x$:

$\sqrt{x^2-4x-5}$

Integrate the following functions w.r.t. $x$:

${\sec }^{2}x·\sqrt{{\tan }^{2}x+\tan x-7}$

Integrate the following functions w.r.t. $x$:

$\sqrt{x^2+2x+5}$

Integrate the following functions w.r.t. $x$:

$\sqrt{2x^2+3x+4}$