integral gral of Find the i Sterns
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integral gral of Find the i Sterns

JEE/Engineering Exams
Maths
Solution
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( int frac{x}{left(x^{2}+1right)^{1 / 3}} d x ) ( quad x^{2}+1=t ) ( Rightarrow 2 x cdot d x=d t ) ( Rightarrow x d x=frac{d t}{2} ) ( therefore int frac{d t / 2}{t^{1 / 3}} ) ( =left(frac{t^{-1 / 3}+1}{-1 / 3+1}right) frac{1}{2}+c ) ( =frac{t^{2 / 3}}{frac{2}{3}} cdot frac{1}{2}+c ) ( =frac{3}{4} t^{2 / 3}+c )
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