00:01
Hello student, in the given question in a bit we have to evaluate the integral as integration of e to the power 2x multiply by x square into dx.
00:11
So, we use the technique of integration by parts to solve the integration by parts involving choosing one part of integral as u term and other part as the dv term.
00:25
So, first let u is equals to x square choose x square as a u term and dv is equals to e to the power 2x into dx.
00:37
Now, differentiate with respect to u.
00:40
So, du is equals to 2x into dx and integrate dv with respect to x as v is equals to 1 by 2 into e to the power of 2 of x.
00:51
Now, we can apply the integration by parts formula as integration of e to the power 2x multiply by x square into du sorry dx is equals to u multiply by v minus integration of v multiply by du.
01:09
Now, plugging into the value.
01:12
So, we get integration of e to the power 2x multiply by x square into dx which is equals to x square multiply by 1 by 2 into e to the power 2x minus integration of 1 by 2 multiply by e to the power 2x multiply by 2x into dx.
01:40
Now, simplifying further.
01:42
So, we get integration of e to the power 2x multiply by x square into d of x which is equals to 1 by 2 into x square multiply by e to the power 2x minus integration of x multiply by e to the power 2x into dx...