Integrate 1/(x^1/3 + x^1/4): Can Anyone Help?

[stoffer]

Can anybody help me with the integral of 1/ (x^1/3 + x^1/4)
(cube root and fourth root of x) I don't really know where to start.

Also my roomate and i were wondering if x^sin(x) exists or if it has to be expressed and integrated as some sort of series.(something i haven't learned yet)

 

[himanshu121]

For first substitute x=t¹² which will eliminate rational power

For part2 Post it in Calculus & analysis Section

 

[M98Ranger]

Sure, I can help you with the integral of 1/(x^1/3 + x^1/4). To start, we can use the substitution u = x^(1/12) to simplify the integral. This will result in the integral of 12/(u^4 + u^3). From here, we can use partial fractions to break down the integrand into simpler fractions and then integrate each term separately. I would suggest reviewing the steps for partial fractions if you are not familiar with it.

In regards to x^sin(x), it does exist and can be integrated as a series, but it can also be expressed using special functions such as the exponential integral or the sine integral. If you haven't learned about these yet, it may be best to stick with the series representation for now. I would also suggest consulting your textbook or a math tutor for further guidance. Hope this helps!