23. ∫(6t - 7)^-2 dt 25. ∫(t^2 + 1)^5 t dt 27. ∫xe^x^2 dx 29....

Transcript

00:01 So, here in this question we have to evaluate the integration in this part 25 where the limit of integration is given to us that is from 2 to 3 t multiply by the sin of t raise to the power dt.

00:14 So, we have to integrate this term.

00:16 So, to find out its integration let us considering that t raise to the power 2 is equals to u.

00:25 So, what we can do from here we have to integrate the t with respect to u.

00:30 So, we can say that dt 2 of t multiply by the dt divided by the du is equals to 1.

00:38 So, from here we can write it as 2t multiply by the dt is equals to du or we can say that t multiply by the dt become equals to du which is divided by 2.

00:51 Then we can plug this value in the given integration.

00:56 So, from here we can if we are considering that t square is equals to u then limit also changes here if we put the value of t as 2.

01:06 So, 2 raise to the power 2 is equals to u.

01:08 So, u from here is equals to 4.

01:10 So, this is the lower limit and when the value of t is equals to 3 then the value of u become equals to 9.

01:17 So, 9 is the upper limit.

01:18 So, plug in to the value here.

01:20 So, i become equals to 1 divided by 2 multiply by the integration of sin of u multiply by the du where the limit is from 4 to 9.

01:30 So, the value of i from here become equals to minus 1 divided by 2 cos of u where the limit of u is from 4 to 9 plus a constant c...

Question

23. \int (6t - 7)^{-2} dt 25. \int (t^2 + 1)^5 t dt 27. \int xe^{x^2} dx 29. \int \frac{1}{5x + 4} dx 31. \int e^{1 - t} dt 33. \int \frac{t}{(3t^2 + 1)^4} dt

Question

23. \int (6t - 7)^{-2} dt 25. \int (t^2 + 1)^5 t dt 27. \int xe^{x^2} dx 29. \int \frac{1}{5x + 4} dx 31. \int e^{1 - t} dt 33. \int \frac{t}{(3t^2 + 1)^4} dt

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