∫√(𝑥/(1 − 𝑥^3 )) 𝑑𝑥 = ∫1▒√𝑥/√(1 − 𝑥^3 ) 𝑑𝑥 Let 𝒕=𝒙^(𝟑/𝟐) Differentiating w.r.t. 𝑥 𝑑𝑡/𝑑𝑥=3/2 𝑥^(3/2 −1) 𝑑𝑡/𝑑𝑥=3/2 𝑥^(1/2 ) 𝑑𝑡/𝑑𝑥=3/2 √𝑥 𝟐/𝟑 𝐝𝐭=√𝒙 𝒅𝒙 Now, our equation becomes ∫1▒√𝑥/√(1 − 𝑥^3 ) 𝑑𝑥=∫1▒〖2/(3√(1 −〖 𝑥〗^3 )) 𝑑𝑡〗 = 𝟐/𝟑 ∫1▒𝒅𝒕/√(𝟏 − 𝒕^𝟐 )dt = 2/3 sin^(−1)⁡〖𝑡+𝑐〗 Putting back 𝑡=𝑥^(3/2) = 𝟐/𝟑 〖𝒔𝒊𝒏〗^(−𝟏)⁡〖〖(𝒙〗^(𝟑/𝟐))+𝒄〗

Next: Question 28 (Choice 2) Important → Ask a doubt

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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