What is the integral of (4x-sin(x)) ?

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

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integral of (4x-sin(x))

\int (4 x - sin (x)) d x

2 x^{2} + cos (x) + C

Solution steps

\int 4 x - 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 x d x - \int sin (x) d x

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

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

= 2 x^{2} - (- cos (x))

Simplify

= 2 x^{2} + cos (x)

Add a constant to the solution

= 2 x^{2} + cos (x) + C

\int_{5}^{1} (- 4 x + 1) d x

x \to 3 - lim (2)

f^{^{'}} = f^{3}

\frac{d}{d x} (x^{- 2} ln (x))

\int_{1}^{4} \frac{x}{x ^{2} + 6 x + 13} d x

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