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

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

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

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

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

Solution steps

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

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

\int C d x = C x

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

Simplify

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

Add a constant to the solution

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

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

\frac{x - 3}{2}

\frac{\partial}{\partial x} (x^{3} y z^{2} + 7 yz)

\frac{d}{d x} (x^{2} e^{x + 3})

y^{^{''}} - 2 y^{^{'}} + y = 1

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