What is the integral of (x^4)/2+cos(x)x ?

The integral of (x^4)/2+cos(x)x is (x^5)/(10)+xsin(x)+cos(x)+C

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integral of (x^4)/2+cos(x)x

\int \frac{x ^{4}}{2} + cos (x) x d x

\frac{x ^{5}}{10} + x sin (x) + cos (x) + C

Solution steps

\int \frac{x ^{4}}{2} + cos (x) x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{x ^{4}}{2} d x + \int cos (x) x d x

\int \frac{x ^{4}}{2} d x = \frac{x ^{5}}{10}

\int cos (x) x d x = x sin (x) + cos (x)

= \frac{x ^{5}}{10} + x sin (x) + cos (x)

Add a constant to the solution

= \frac{x ^{5}}{10} + x sin (x) + cos (x) + C

\frac{\partial}{\partial x} (\frac{x y}{2})

f (x) = 5 x - 4 x, (1, 1)

sin (x) y^{^{'}} + cos (x) y = 0

\frac{9 s}{( s + 9 ) ^{2}}

\int (ln (x)) x d x

What is the integral of (x^4)/2+cos(x)x ?
The integral of (x^4)/2+cos(x)x is (x^5)/(10)+xsin(x)+cos(x)+C