What is the integral of-1/2*sin(2x)+1/4*2x ?

The integral of-1/2*sin(2x)+1/4*2x is 1/4 cos(2x)+(x^2)/4+C

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integral of-1/2sin(2x)+1/42x

\int - \frac{1}{2} \cdot sin (2 x) + \frac{1}{4} \cdot 2 x d x

\frac{1}{4} cos (2 x) + \frac{x ^{2}}{4} + C

Solution steps

\int - \frac{1}{2} sin (2 x) + \frac{1}{4} \cdot 2 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 \frac{1}{2} sin (2 x) d x + \int \frac{1}{4} \cdot 2 x d x

\int \frac{1}{2} sin (2 x) d x = - \frac{1}{4} cos (2 x)

\int \frac{1}{4} \cdot 2 x d x = \frac{x ^{2}}{4}

= - (- \frac{1}{4} cos (2 x)) + \frac{x ^{2}}{4}

Simplify

= \frac{1}{4} cos (2 x) + \frac{x ^{2}}{4}

Add a constant to the solution

= \frac{1}{4} cos (2 x) + \frac{x ^{2}}{4} + C

\int x^{5} + 1 d x

\int e^{t a n (3 x)} sec^{2} (3 x) d x

\frac{d}{d x} (\frac{f ( x ) g ( x )}{x})

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

\int_{0}^{l n (8)} x e^{x} d x

What is the integral of-1/2*sin(2x)+1/4*2x ?
The integral of-1/2*sin(2x)+1/4*2x is 1/4 cos(2x)+(x^2)/4+C