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Grade 12Integral Calculus

We have to find the integral of 3x⁴-1/(x⁴+x+1)² options are
1) x/(x⁴+x+1)
2) -x/(x⁴+x+1)
3) x+1/(x⁴+x+1)
4) -x-1/(x⁴+x+1)

Question image for We have to find the integral of 3x⁴-1/(x⁴+x+1)² o

Neha Sharma

7 Years agoGrade 12

1 Answer

Aditya Gupta

7 Years ago

Divide the numerator and denominator by x^2.

We get

(3x^2-1/x^2)/(x^3+1+1/x)^2

Now put x^3+1+1/x= y

So integral becomes dy/y^2

So final answer is

-x/(x^4+x+1)+C

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