How do you find the integral of $x*sqrt(25+x^2)$ ?

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Answer 1 · 2015-04-06T19:55:43

Have a look but please check my maths:
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Answer 2 · 2015-04-06T20:34:25

$int xsqrt(25 + x^2)dx = int1/2*2xsqrt(25 + x^2)dx$

$= int1/2sqrt(25 + x^2)*(2xdx)$
$= int1/2sqrt(25 + x^2)*d(25 + x^2)$

$=1/2int(25 + x^2)^(1/2)*d(25 + x^2)$

$= 1/2((25 + x^2)^(3/2))/(3/2) + c$

$=((25 + x^2)^(3/2))/3 + c$

How do you find the integral of x*sqrt(25+x^2)x*sqrt(25+x^2)?