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

The integral of 4+x^2+sin(x) is 4x+(x^3)/3-cos(x)+C

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integral of 4+x^2+sin(x)

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

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

Solution steps

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

\int 4 d x = 4 x

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

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

= 4 x + \frac{x ^{3}}{3} - cos (x)

Add a constant to the solution

= 4 x + \frac{x ^{3}}{3} - cos (x) + C

What is the integral of 4+x^2+sin(x) ?
The integral of 4+x^2+sin(x) is 4x+(x^3)/3-cos(x)+C