How do you integrate $\int sin \sqrt{x}$ $int sinsqrtx$ by parts?

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How do you integrate $\int sin \sqrt{x}$ $int sinsqrtx$ by parts?

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Answer 1 · 2018-06-02T13:49:57

$2 \sqrt{x} \cdot cos (\sqrt{x}) - 2 sin (\sqrt{x}) + C$ $2sqrt(x)*cos(sqrt(x))-2sin(sqrt(x))+C$

Explanation:

Substituting $t = \sqrt{x}$ $t=sqrt(x)$ then we get
$d x = 2 t d t$ $dx=2tdt$
and we have to solve
$2 \int t sin (t) d t$ $2int tsin(t)dt$
By partial Integration we get
$\int t sin (t) d t = t cos (t) - \int cos (t) d t$ $int tsin(t)dt=tcos(t)-intcos(t)dt$
so we get
$2 t cos (t) - 2 sin (t) + C$ $2tcos(t)-2sin(t)+C$
$2 \sqrt{x} cos (\sqrt{x}) - 2 sin (\sqrt{x}) + C$ $2sqrt(x)cos(sqrt(x))-2sin(sqrt(x))+C$

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How do you integrate $\int sin \sqrt{x}$ $int sinsqrtx$ by parts?

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