Find the indefinite integral by making the substitution .

Question

Find the indefinite integral by making the substitution  . ​  ​

Quizplus · Accepted Answer

Let u = 11eac44f_ec73_21e5_bedf_d704176e984a_TB7497_11, then du = 11eac44f_ec73_48f6_bedf_33dc8555c0e1_TB7497_11 dx. Substituting u and du into the integral, we get:
∫(11eac44f_ec73_21e5_bedf_d704176e984a_TB7497_11)/(√(11eac44f_ec73_21e5_bedf_d704176e984a_TB7497_11 - 3)) 11eac44f_ec73_48f6_bedf_33dc8555c0e1_TB7497_11 dx
= (1/2) ∫(2/√u)(du) [since 11eac44f_ec73_21e5_bedf_d704176e984a_TB7497_11 - 3 = u]
= ∫(1/u^(1/2))(du)
= 11eac44f_ec73_700a_bedf_e3f7fd381471_TB7497_11u^(1/2) + C
= 11eac44f_ec73_700a_bedf_e3f7fd381471_TB7497_11√(11eac44f_ec73_21e5_bedf_d704176e984a_TB7497_11 - 3) + C
= Choice (D)

Find the Indefinite Integral by Making the Substitution