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how to integrate 1/(1+x^3)^1/2

how to integrate 1/(1+x^3)^1/2

Grade:

1 Answers

Pramod J AskiitiansExpert-IIT-B
36 Points
10 years ago

Dear student,

let (1+x^3) = t^2

=> 3x^2*dx = 2tdt

=> dx = 2tdt/3x^2

substitute this in integral euation,

∫(1+x^3)^-1/2 * 2tdt/3x^2

=> ∫ 2dt/3*(t-1)^(2/3)

put t-1 = k

=> ∫ 2*dk/3*k^(2/3)

=> 2k^1/3

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