Question

Integrate the integral below:

Answer 1

below where?

Answer 2

\[\int\limits\limits_{}^{}\frac{ dy }{ \sqrt{y}+\sqrt[4]{y ^{3}} }\]

Answer 3

Please do note that Integration by substitution was just introduced to us so I may not be able to understand an explanation right away. :)

Answer 4

u dont need integration by substitution

Answer 5

what method can I use?
Sorry, I just assumed that it is what is needed because it is our current topic

Answer 6

I would use the substitution
\[y=t^2\Rightarrow dy=2tdt\]
Try it.

Answer 7

There is another better,
\[y=t^4\Rightarrow dy=4t^3dt\]

Answer 8

\[\int\frac{4t^3dt}{t^2+t^3}=\int\frac{4tdt}{1+t}=4\int\frac{(1+t-1)dt}{1+t}=\\
=4\int\left(1-\frac{1}{1+t}\right)dt=4t-4\ln|1+t|+K=\\
=4\sqrt[4]{y}-4\ln|1+\sqrt[4]{y}|+K\]