Question

Can someone check my answer?

Answer 1

integral (((2+sqrt(x))^6))/(sqrt (x))) dx = ?

Answer 2

My answer is either (2/7) (2+x^(1/2))^7 + C or none of these (from other given options).

Answer 3

Here's why I have a problem: http://www.wolframalpha.com/input/?i=%28integral+%28%28%282%2Bsqrt%28x%29%29%5E6%29%2F%28sqrt%28x%29%29%29dx%29+%3D+%282%2F7%29+%282%2Bx%5E%281%2F2%29%29%5E7

Answer 4

Does the +256/7 make it none of the above?

Answer 5

@dumbcow

Answer 6

you mean that:
\[\int \frac{(2+\sqrt{x})^6 dx}{\sqrt{x}}\]
?

Answer 7

yes

Answer 8

Ok, do this:
\[u=\sqrt{x} \Rightarrow du = \frac{1}{2\sqrt{x}}dx\]

Answer 9

then we got:
\[2\int (2+u)^6 du\]

Answer 10

now, if you still can't see the result, do this:
\(v = 2+u \Rightarrow dv = du\), so
\[2\int v^6 dv = \frac{2}{7}v^7 + c =\frac{2}{7}(2+u)^7 +c= \frac{2}{7}(2+\sqrt{x})^7 +c \]

Answer 11

Got it?

Answer 12

Hint: you always substitute unti you get a simple integral you can evaluate.

Answer 13

Yes so I guess I was right, it was not none of these.