Evaluate the integral"

$$\int _{0}^{1} \frac{7x^4+5x^2+4x}{\sqrt {x^3+x+1}} dx$$

I am not able to proceed in this question. Could someone give me some hint?

Edit: Initially as I wasn't able to proceed and that is why I couldn't show my work but I did not requested for answer but some hint and then with little suggestion from @Andreas I was able to solve the question and posted answer here as well.

I don't think it should be put on hold as an off-topic because even after downvotes from some users it is still having $+2$ upvotes. Please consider my request.


closed as off-topic by heropup, mlc, C. Falcon, Zain Patel, Jyrki Lahtonen May 10 '17 at 5:35

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  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – heropup, mlc, C. Falcon, Zain Patel, Jyrki Lahtonen
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  • $\begingroup$ Have you tried Wolfram yet? What does it spit out? $\endgroup$ – John Smith May 9 '17 at 21:16
  • $\begingroup$ Here is it your answer. wolframalpha.com/input/… $\endgroup$ – Crostul May 9 '17 at 21:18
  • $\begingroup$ What substitutions have you thought of using? $\endgroup$ – projectilemotion May 9 '17 at 21:32
  • 4
    $\begingroup$ It's a good idea to use Wolfram's result and do "reverse engineering" to arrive there, using the usual integration rules. $\endgroup$ – Andreas May 9 '17 at 21:35
  • $\begingroup$ @Andreas Thank you for the suggestion. Dividing and multiplying by $x^2$ will do the trick. But I think it is tough to obverse it without looking at the answer. $\endgroup$ – Mathematics May 9 '17 at 21:59

With Andreas's suggestion, I have reached the answer.

We divide and multiply by $x^2$, the expression inside square root in denominator

becomes $x^7+x^5+x^4$ and we set $x^7+x^5+x^4=t$ to get $(7x^6+5x^4+4x^3).dx=dt$ which is present in numerator.


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