Asked by Wawen
Please solve it step by step. Integrate:
∫(x^3/(√(x^2+1))dx
∫(x^3/(√(x^2+1))dx
Answers
Answered by
Steve
x = tanθ
x^2+1 = sec^2θ
dx = sec^2θ dθ
and now your integrand becomes
tan^3θ/secθ * sec^2θ dθ
= tan^3θ secθ dθ
= tan^2θ (secθ tanθ dθ)
= (sec^2θ - 1) (secθ tanθ dθ)
let u = secθ
du = secθ tanθ dθ
and now you have just
(u^2-1) du
x^2+1 = sec^2θ
dx = sec^2θ dθ
and now your integrand becomes
tan^3θ/secθ * sec^2θ dθ
= tan^3θ secθ dθ
= tan^2θ (secθ tanθ dθ)
= (sec^2θ - 1) (secθ tanθ dθ)
let u = secθ
du = secθ tanθ dθ
and now you have just
(u^2-1) du
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