What is the integral of sqrt(x)*cos(x) ?

The integral of sqrt(x)*cos(x) is sqrt(x)sin(x)-sqrt(pi/2)\S(sqrt(2/pi)sqrt(x))+C

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integral of sqrt(x)*cos(x)

\int x \cdot cos (x) d x

x sin (x) - \frac{π}{2} § (\frac{2}{π} x) + C

Solution steps

\int x cos (x) d x

Apply Integration By Parts

: x sin (x) - \int \frac{sin ( x )}{2 x} d x

= x sin (x) - \int \frac{sin ( x )}{2 x} d x

\int \frac{sin ( x )}{2 x} d x = \frac{π}{2} § (\frac{2}{π} x)

= x sin (x) - \frac{π}{2} § (\frac{2}{π} x)

Add a constant to the solution

= x sin (x) - \frac{π}{2} § (\frac{2}{π} x) + C

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\int \frac{x ^{4} - 3 x}{x} d x

\int \frac{5 x ^{2} + 30 x + 43}{( x + 3 ) ^{3}} d x

What is the integral of sqrt(x)*cos(x) ?
The integral of sqrt(x)*cos(x) is sqrt(x)sin(x)-sqrt(pi/2)\S(sqrt(2/pi)sqrt(x))+C