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Solve integrations by substitution 4 on top ∫ 0 on bottom x sqrt(x^2+9) dx where u=x^2+9?
Please include all the steps and explanations! Thanks!
u = x^2 + 9
du = 2xdx
du/2x = dx ( Use this equation and this u = x^2 + 9)
When x =0 , u = 0^2 + 9
x =4 , u = 4^2 +9 = 25
∫ x sqrt(x^2+9) dx = ∫ 25 on top 9 on bottom x sqrt(u) du/2x = (1/2)∫ sqrt(u)du
= (1/2) * (2/3) u^(3/2)
= (1/3)* u^(3/2) [ evaluted at 25 and 9] = (1/3)* [ 5^3 - 3^3] = 1/3 [ 125 - 27] = 98/3
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