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

The integral of ((x^2)/2+sin(x)) is (x^3)/6-cos(x)+C

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integral of ((x^2)/2+sin(x))

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

\frac{x ^{3}}{6} - cos (x) + C

Solution steps

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

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

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

= \frac{x ^{3}}{6} - cos (x)

Add a constant to the solution

= \frac{x ^{3}}{6} - cos (x) + C

\frac{\partial}{\partial x} (e^{4 x yz - 9})

\frac{2 x + 6 x ^{2}}{( 1 + 6 x ) ^{2}}

x^{3} + 3 x^{2} + x + 3

\int_{0}^{2} x^{3} - x d x

x^{3} + x^{2} - x - 3, at x = - 2

What is the integral of ((x^2)/2+sin(x)) ?
The integral of ((x^2)/2+sin(x)) is (x^3)/6-cos(x)+C