Question

\[\int\limits_{0}^{2}\left(\begin{matrix}3x \\ x ^{2}+4\end{matrix}\right)\]

Answer 1

\[\int\limits\frac{3x}{x^{2}-4} dx\]
Not a matrices?

Answer 2

\[\int\limits\frac{3x}{x^{2}+4} dx\]

Answer 3

yup. :) but it is a definite integration. :)

Answer 4

let \(u=x^2+4\) => \[dx= \frac{du}{2x} \]

Answer 5

answer? :)

Answer 6

answer @Mimi_x3 ? :)

Answer 7

\[\int\limits\frac{3x}{u} * \frac{du}{2x} => \int\limits\frac{3\cancel{x}}{u} * \frac{du}{2\cancel{x}} => \frac{3}{2} \int\limits\frac{1}{u} du\]

Answer 8

you may take 3 out
then take 1/2 common such that 1/2 is out and inside there is 2x
now x^2 + 4 =t
so 2xdx = dt
=> 3/2 (dt/t)
try now..

Answer 9

just what @Mimi_x3 says :-)

Answer 10

Integrate that then don't forget to sub back in the \(u\). (:

Answer 11

ok thanks @Mimi_x3 :)