Posted by **W** on Monday, January 2, 2012 at 8:15pm.

Integrate (1/2)sin(x^(1/2))dx.

I've tried using u-substitution, with u=sin(x^(1/2)). du would then = ((1/2)x^(-1/2))(cos(x^(1/2))). As you can see, this only make the problem more complicated. I don't get what to do. Thank you in advance!

- Calculus -
**Damon**, Monday, January 2, 2012 at 8:28pm
when all else fails

go to wolfram alpha (Just type that in your browser)

in the box type:

Integrate (1/2)sin(x^(1/2))

after you see the answer, click on "show steps" in the box on the upper right.

- Calculus -
**Damon**, Monday, January 2, 2012 at 8:30pm
integral (sin(sqrt(x)))\/2 dx = sin(sqrt(x))-sqrt(x) cos(sqrt(x))+constant

Possible intermediate steps:\n integral (sin(sqrt(x)))\/2 dx\nFactor out constants:\n = 1\/2 integral sin(sqrt(x)) dx\nFor the integrand sin(sqrt(x)), substitute u = sqrt(x) and du = 1\/(2 sqrt(x)) dx:\n = integral u sin(u) du\nFor the integrand u sin(u), integrate by parts, integral f dg = f g- integral g df, where \n f = u, dg = sin(u) du,\n df = du, g = -cos(u):\n = integral cos(u) du-u cos(u)\nThe integral of cos(u) is sin(u):\n = sin(u)-u cos(u)+constant\nSubstitute back for u = sqrt(x):\n = sin(sqrt(x))-sqrt(x) cos(sqrt(x))+constant

- Calculus -
**Damon**, Monday, January 2, 2012 at 8:31pm
Obviously it does not copy and paste very well so go to the original. Your substitution approach was in fact what was used.

- Calculus -
**bobpursley**, Monday, January 2, 2012 at 8:33pm
let u= sqrtx

du= 1/2*1/sqrtx dx

dx= 2u du

INT 1/2 sin (sqrtx) dx

INT 1/2 sin u 2u du

int u sin u du=-u cos u + sin u

then change it back to x

-sqrtx cosSqrtx+sinsqrtx

check: take the derivative...

-1cossqrtx/2sqrx+ -sqrtx(-sinsqrtx)1/2sqrx +cossqurx/2sqrtx

-1/2(-sinSqrtx)

1/2 sinSqrtx so it checks.

- Calculus -
**W**, Monday, January 2, 2012 at 8:45pm
very cool. Thanks, both of you! Does wolfram alpha give steps for all integration problems?

- Calculus -
**Damon**, Monday, January 2, 2012 at 8:51pm
Pretty much so

your other one would be

integrate 1/(x ln x)

- Calculus -
**W**, Monday, January 2, 2012 at 9:13pm
awesome! Thanks Damon ;D

## Answer This Question

## Related Questions

- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- algebra - Can someone please help me do this problem? That would be great! ...
- tigonometry - expres the following as sums and differences of sines or cosines ...
- Calculus - I have two questions, because I'm preparing for a math test on monday...
- Calculus - Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I ...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- Trigonometry - Solve the equation for solutions in the interval 0<=theta<...
- Precal - I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A...
- calculus - 1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...

More Related Questions