This is a Rhetorical question since I already know that the answer is because the inner function: $$(1+x^2)$$ is not linear.

But what I want to know is a $why$ it must be linear. I have scoured the internet and maths books rigorously looking for an answer to this but no such luck. So if someone could kindly explain to me in simple english (if possible) why it must be linear and why $$\int(1+x^2)^4\mathrm dx$$ is not equal to $$\frac{(1+x^2)^{5}}{5(2x)}+C?$$

Any responses appreciated,

Many Thanks.

regards,

BLAZE.