What is the integral of (sin(x)+2x) ?

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

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integral of (sin(x)+2x)

\int (sin (x) + 2 x) d x

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

Solution steps

\int sin (x) + 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 sin (x) d x + \int 2 x d x

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

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

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

Add a constant to the solution

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

\int \frac{5 x - 1}{x ( x - 3 ) ^{2} ( x + 2 ) ^{2}} d x

\int \frac{1}{3 x ^{2} + 12} d x

\int \frac{2 x ^{3} + 1}{x ^{2} - 4 x} d x

\int (tan (θ) + sec (θ))^{2} d θ

\int 2 1 - 25 x^{2} d x

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