A Variable Suddenly Appears

[ninguen]

Doing another problem from Schaum's.

I'd pay for a video series that goes through Schaum's problems one-by-one. These problems seem much tougher than stuff i see on youtube.

Right now, I've got the following question:

(Squiggly integral thing) (1+x^2)/x^1/2 dx

When I divide the top by the bottom, I get:

(Squiggly integral thing) x^-1/2 + x^3/2 dx

When I do the integral, I get

2 x^1/2 + 2/5 x^5/2 + C

or

2x^1/2 (1+ 1/5 x^2) + C

But the official answer according to Schaum's is

2x^1/2 (1+ + 2/3 x + 1/5 x^2) + C

So where the heck did the 2/3 x come from? Did I make a careless mistake?

 

[galactus]

The original problem is \(\displaystyle \displaystyle\int\frac{x^{2}+1}{\sqrt{x}}dx=\frac{2\sqrt{x}(x^{2}+5)}{5}\)


It would appear there is a typo in Schaum.

Their solution would correspond to \(\displaystyle \displaystyle\int\frac{x^{2}+2x+1}{\sqrt{x}}\)

Apparently, they left out a 2x in the original integrand. Or something to that effect.

 

[Deleted member 4993]

Doing another problem from Schaum's.

I'd pay for a video series that goes through Schaum's problems one-by-one. These problems seem much tougher than stuff i see on youtube.

Right now, I've got the following question:

(Squiggly integral thing) (1+x^2)/x^1/2 dx

When I divide the top by the bottom, I get:

(Squiggly integral thing) x^-1/2 + x^3/2 dx

When I do the integral, I get

2 x^1/2 + 2/5 x^5/2 + C

or

2x^1/2 (1+ 1/5 x^2) + C

But the official answer according to Schaum's is

2x^1/2 (1+ + 2/3 x + 1/5 x^2) + C

So where the heck did the 2/3 x come from? Did I make a careless mistake?

First of all, although Schaum series books are generally excellent learning tool - those have bucket ful of "mis-prints"

Are you sure your problem was NOT:

\(\displaystyle \display\int \frac{(1+x)^2}{\sqrt{x}} dx\)

 

[ninguen]

Are you sure your problem was NOT:

\(\displaystyle \display\int \frac{(1+x)^2}{\sqrt{x}} dx\)

Of course i'm not. I don't know calculus!

Thanks guys. It's frustrating fumbling around in the dark when you don't know if you can trust the learning tools you're given.