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2 Answers
- fernando_007Lv 68 years agoFavorite Answer
integral[sqrt(x)/(x+1)] =
| first substitution y=sqrt(x) => dy=(1/2)*dx/sqrt(x) => dx=2*y*dy |
= integral[2*y^2*dy/(y^2+1)] = 2*integral[(1 - 1/(y^2+1))*dy =
= 2*y - 2*integral[dy/(y^2+1)]
| second substitution: y=tg(z) => dy=(1+tg^2(z))*dz | =
= 2*y - 2*integral[dz] = 2*y - 2*z =
= 2*[sqrt(x) - arctan(sqrt(x)]
- JJWJLv 78 years ago
Step one: Remove the sqrt term by writing down
Let y = sqrt(x). Replace sqrt(x), replace x+1 AND replace dx assuming you meant to follow the function with "dx".
That should get you started.
