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Integrals

Question

Evaluate: $\int \frac{x^{2}}{1 + x^{3}} dx$

Solution

$\int \frac{x^{2}}{1 + x^{3}} dx Let 1 + x^{3} = t \Rightarrow 0 + 3 x^{2} dx = dt \Rightarrow x^{2} dx = \frac{dt}{3} ∴ \int (\frac{x^{2}}{1 + x^{3}}) dx = \int \frac{\frac{dt}{3}}{t} = \frac{1}{3} \int \frac{dt}{t} = \frac{1}{3} \log |t| + c = \frac{1}{3} \log |1 + x^{3}| + c$

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Integrals

Evaluate: $\int \frac{x^{2}}{1 + x^{3}} dx$

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Integrals

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Some More Questions From Integrals Chapter

Mock Test Series

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Entrance Exams Preparation

Evaluate: $\int \frac{x^{2}}{1 + x^{3}} dx$