Integration by parts tricky problems

[machete]

Hi guys, I'm trying to solve some integrals by using the integration by parts method

\(\displaystyle \mbox{a }\, \int\, \left[2x\, \sqrt{2x\,}\, -\, 3\right]\, dx\)

\(\displaystyle \mbox{b }\, \int\, \left[x\,e^{x^2}\right]\, dx\)

\(\displaystyle \mbox{c }\, \int\, \left[x\,e^x\right]\, dx\)

\(\displaystyle \mbox{d }\, \int\, \left[x^3\, e^{2x}\right]\, dx\)

\(\displaystyle \mbox{e }\, \int\, \left[x\, \ln(x\, +\, 1)\right]\, dx\)

\(\displaystyle \mbox{f }\, \int\, \left[x^2\, sen(x)\right]\, dx\)

\(\displaystyle \mbox{g }\, \int\, \left[\tan^2(x)\, \sec(x)\right]\, dx\)

it's been a while since I tried this kind of integrals, I wonder if anyone knows the anwser and the whole procedure.

Thank you in advance

 

[stapel]

it's been a while since I tried this kind of integrals, I wonder if anyone knows the anwser and the whole procedure.

Probably quite a few here are familiar with "the whole procedure". However, this is not our homework; it's yours.

Hi guys, I'm trying to solve some integrals by using the integration by parts method

\(\displaystyle \mbox{a) }\, \int\, \left[2x\, \sqrt{2x\,}\, -\, 3\right]\, dx\)

\(\displaystyle \mbox{b) }\, \int\, \left[x\,e^{x^2}\right]\, dx\)

\(\displaystyle \mbox{c) }\, \int\, \left[x\,e^x\right]\, dx\)

\(\displaystyle \mbox{d) }\, \int\, \left[x^3\, e^{2x}\right]\, dx\)

\(\displaystyle \mbox{e) }\, \int\, \left[x\, \ln(x\, +\, 1)\right]\, dx\)

\(\displaystyle \mbox{f) }\, \int\, \left[x^2\, sen(x)\right]\, dx\)

\(\displaystyle \mbox{g) }\, \int\, \left[\tan^2(x)\, \sec(x)\right]\, dx\)

To learn how to do integration by parts, try some of the lessons in this listing.

Once you have studied at least two lessons from the link, please attempt the exercises. For instance, you would start (a) by noting the common element of "2x", setting 2x = u so 2dx = du and dx = (1/2)du, and doing the substitution:

. . . . .\(\displaystyle \mbox{a') }\, \int\, \left[u^{\frac{3}{2}}\, -\, 3\right]\, \left(\dfrac{1}{2}\right)\, dx\)

. . . . . . . .$\displaystyle =\, \left(\dfrac{1}{2}\right)\, \int\, u^{\frac{3}{2}}\, du\, -\, \left(\dfrac{1}{2}\right)\, \int\,3\, du$

. . . . . . . .$\displaystyle =\, \left(\dfrac{1}{2}\right)\, \left(\dfrac{2}{5}\right)\, u^{\frac{5}{2}}\, -\, \left(\dfrac{1}{2}\right)\, 3u$

. . . . . . . .$\displaystyle =\, \left(\dfrac{1}{2}\right)\, \left(\dfrac{2}{5}\right)\, (2x)^{\frac{5}{2}}\, -\, \left(\dfrac{1}{2}\right)\, (3 \cdot 2x)$

...and so forth.

If you get stuck, you can then reply with a clear listing of your efforts so far, at which point we can being to work with you. Thank you!

 

[Deleted member 4993]

Hi guys, I'm trying to solve some integrals by using the integration by parts method

\(\displaystyle \mbox{a }\, \int\, \left[2x\, \sqrt{2x\,}\, -\, 3\right]\, dx\)

\(\displaystyle \mbox{b }\, \int\, \left[x\,e^{x^2}\right]\, dx\)

\(\displaystyle \mbox{c }\, \int\, \left[x\,e^x\right]\, dx\)

\(\displaystyle \mbox{d }\, \int\, \left[x^3\, e^{2x}\right]\, dx\)

\(\displaystyle \mbox{e }\, \int\, \left[x\, \ln(x\, +\, 1)\right]\, dx\)

\(\displaystyle \mbox{f }\, \int\, \left[x^2\, sen(x)\right]\, dx\)

\(\displaystyle \mbox{g }\, \int\, \left[\tan^2(x)\, \sec(x)\right]\, dx\)

it's been a while since I tried this kind of integrals, I wonder if anyone knows the anwser and the whole procedure.

Thank you in advance

What is sen?

 

[Nazariy]

What is sen?

I bet it's $\displaystyle \sin x$

 

[Ishuda]

What is sen?

Spanish/Italian for sin(x)