# Thread: A Couple Integral Problems I'm Stuck On

1. ## A Couple Integral Problems I'm Stuck On

Hey, hope you are all well this fine evening

I've been working on some homework problems for tomorrow, and I am absolutely stuck on two of them.

1) integral of (1+sinx) / (1-sinx)

For this one, I couldn't come up with any trig identities that would help. I thought about squaring the numerator and denominator but I have no idea if you can do that for integrals haha. Hopefully you guys would know hehe

2) integral of ((x^5)(e^(-x^3))

For this one, I tried integration by parts but ended up with a larger exponent somewhere down the road, so I figured I was just thinking about it incorrectly. And I can't do the tabular method because I can't integrate e^(-x^3)). My next guess was u-substitution but I'm just not seeing how to apply it.

The book says that these are all "elementary functions" so no series needed. I think I'm just dumb haha. Any help would be awesome. Thanks guys

2. Originally Posted by coolguy9
Hey, hope you are all well this fine evening

I've been working on some homework problems for tomorrow, and I am absolutely stuck on two of them.

1) integral of (1+sinx) / (1-sinx)

For this one, I couldn't come up with any trig identities that would help. I thought about squaring the numerator and denominator but I have no idea if you can do that for integrals haha. Hopefully you guys would know hehe

2) integral of ((x^5)(e^(-x^3))

For this one, I tried integration by parts but ended up with a larger exponent somewhere down the road, so I figured I was just thinking about it incorrectly. And I can't do the tabular method because I can't integrate e^(-x^3)). My next guess was u-substitution but I'm just not seeing how to apply it.

The book says that these are all "elementary functions" so no series needed. I think I'm just dumb haha. Any help would be awesome. Thanks guys
#1 multiply top and bottom by $\frac{1+ \sin x}{1 + \sin x}$ and use and identity on the bottom.

#2, try the substitution $u = -x^3$

3. $\frac{1+\sin{x}}{1-\sin{x}} \cdot \frac{1+\sin{x}}{1+\sin{x}} =
$

$\frac{1 + 2\sin{x} + \sin^2{x}}{1 -\sin^2{x}} =
$

$\frac{1 + 2\sin{x} + \sin^2{x}}{\cos^2{x}} =$

$\sec^2{x} + 2\sec{x}\tan{x} + \tan^2{x} =$

$2\sec^2{x} + 2\sec{x}\tan{x} - 1$

last expression should be easy to integrate.

$x^5 \cdot e^{-x^3} =$

$x^3 \cdot x^2 \cdot e^{-x^3}$

let $t = x^3$ ... $dt = 3x^2 \, dx$

$\frac{1}{3} \int t \cdot e^{-t} \, dt$

now use tabular.

4. Ah, you guys are life savers. Thanks to the both of you

In regards to the u = -x^3, I just didn't see to split up the x^5. Bad miss on my part hehe

Anyways, thanks again