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))

Simplify

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

Add a constant to the solution

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

\int \frac{1}{cos ^{2} ( 5 x )} d x

x \to 1 lim (\frac{2 \cdot x + 3}{x + 4})

\int \frac{x + 1}{3 - 2 x - x ^{2}} d x

\frac{\partial}{\partial y} (e^{x y} tan (y))

\frac{d}{d x} (1 + \frac{5 e ^{- 2 x^{2}}}{2 - ∣ x ∣})

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