What is the integral of x^3+sin(x) ?

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

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integral of x^3+sin(x)

\int x^{3} + sin (x) d x

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

Solution steps

\int x^{3} + 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 x^{3} d x + \int sin (x) d x

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{sin ( x )}{x})

(2 x^{2} + 1)^{3} \cdot (x^{2} - 1)

2 x + 4, 2 - 3 x, - x

f (x) = 12 (x - (\frac{1}{x})^{4}), at x = 2

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