What is the integral of $\int [x \cdot cos (x^{2})] (d x)$ $int [x * cos(x^2)](dx)$ ?

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What is the integral of $\int [x \cdot cos (x^{2})] (d x)$ $int [x * cos(x^2)](dx)$ ?

1 Answer

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Answer 1 · 2016-03-19T10:00:21

$= \frac{1}{2} sin (x^{2}) + C$ $=1/2sin(x^2)+C$

Explanation:

Let
$z = x^{2}$ $z=x^2$
then
$\Rightarrow d z = 2 x d x$ $=>dz=2xdx$
substituting $x d x = \frac{d z}{2} and x^{2} = z$ $xdx=(dz)/2 and x^2=z$
we have
$I = \frac{1}{2} \int cos (z) d z = \frac{1}{2} sin z + C = \frac{1}{2} sin (x^{2}) + C$ $I=1/2intcos(z)dz=1/2sinz +C=1/2sin(x^2)+C$

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What is the integral of $\int [x \cdot cos (x^{2})] (d x)$ $int [x * cos(x^2)](dx)$ ?

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What is the integral of $\int [x \cdot cos (x^{2})] (d x)$ $int [x * cos(x^2)](dx)$ ?