If ∫$$dx1+x+13=32(x+1)2/3$$−$$3(x+1)1/3+f(x)+C$$ then $$f(x)$$ is equal to

Correct option is 23log⁡|1+x+13|

Questions

If $\int \frac{d x}{1 + \sqrt[3]{x + 1}} = \frac{3}{2} (x + 1)^{2 / 3} - 3 (x + 1)^{1 / 3}$
$+ f (x) + C then f (x)$ is equal to

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detailed solution

Correct option is B

Put x+1=t3, we have∫dx1+x+13=∫3t2dt1+t=3∫t−1+11+tdt=3t22−t+log⁡|1+t|+C=32(x+1)2/3−3(x+1)1/3+3log⁡|1+x+13|+C

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If ∫dx1+x+13=32(x+1)2/3−3(x+1)1/3+f(x)+C then f(x) is equal to

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Ready to Test Your Skills?

free study material

If $\int \frac{d x}{1 + \sqrt[3]{x + 1}} = \frac{3}{2} (x + 1)^{2 / 3} - 3 (x + 1)^{1 / 3}$
$+ f (x) + C then f (x)$ is equal to