SOLUTION: integrate (1)/(sqrt (x)+(x)(sqrt(x))) dx

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Question 906055: integrate (1)/(sqrt (x)+(x)(sqrt(x))) dx
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
int%28dx%2F%28sqrt%28x%29%2Bx%2Asqrt%28x%29%29%29

int%28dx%2F%28+sqrt%28x%29%281%2Bx%29+%29%29

Let u=sqrt%28x%29, u%5E2=x
    matrix%282%2C1%2C%22%22%2Cu=x%5E%281%2F2%29%29
    matrix%282%2C1%2C%22%22%2Cdu=expr%281%2F2%29x%5E%28-1%2F2%29dx%29
    du=dx%2F%282x%5E%221%2F2%22%29
    du=dx%2F%282sqrt%28x%29%29
    du=dx%2F%282u%29
    2u%2Adu=dx

Substitute for x, dx, and sqrt%28x%29

int%282u%2Adu%2F%28u%281%2Bu%5E2%29%29%29 

int%282cross%28u%29%2Adu%2F%28cross%28u%29%281%2Bu%5E2%29%29%29

int%282du%2F%281%2Bu%5E2%29%29

2int%28du%2F%281%2Bu%5E2%29%29

2%2Aexpr%281%2F1%29arctan%28u%2F1%29%2BC

2arctan%28u%29%2BC

2arctan%28sqrt%28x%29%29%2BC

Edwin