Find \(\int \frac{20x^3}{1+x^4} dx\).(a) 5 log⁡(x^4)+C(b) -5 log⁡(1+x^4)+C(c) 5 log⁡(1+x^4)+C(d) log⁡(1+x^4)+CI had been asked this question in class test.My question is taken from Methods of Integration-1 in division Integrals of Mathematics – Class 12

Find \(\int \frac{20x^3}{1+x^4} dx\).(a) 5 log⁡(x^4)+C(b) -5 log⁡(

1.	Find \(\int \frac{20x^3}{1+x^4} dx\).(a) 5 log⁡(x^4)+C(b) -5 log⁡(1+x^4)+C(c) 5 log⁡(1+x^4)+C(d) log⁡(1+x^4)+CI had been asked this question in class test.My question is taken from Methods of Integration-1 in division Integrals of Mathematics – Class 12
Answer» CORRECT ANSWER is (c) 5 log⁡(1+x^4)+C To ELABORATE: Let 1+x^4=t 4x^3 dx=DT ∴\(\int \frac{20x^3}{1+x^4} dx=5\int \frac{dt}{t}\) =5 log⁡t Replacing t with 1+x^4, we get \(\int \frac{20x^3}{1+x^4} dx=5 \,log⁡(1+x^4)+C\)

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