What is the integral of 2x+6cos(x) ?

The integral of 2x+6cos(x) is x^2+6sin(x)+C

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integral of 2x+6cos(x)

\int 2 x + 6 cos (x) d x

x^{2} + 6 sin (x) + C

Solution steps

\int 2 x + 6 cos (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 2 x d x + \int 6 cos (x) d x

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

\int 6 cos (x) d x = 6 sin (x)

= x^{2} + 6 sin (x)

Add a constant to the solution

= x^{2} + 6 sin (x) + C

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

\int - \frac{2}{81 - 49 t ^{2}} d t

\frac{d}{d x} (\frac{x ^{6}}{x ^{2}})

\int \frac{x ^{2} - 9}{x} d x

y = \frac{1}{x ^{2} + 1}

What is the integral of 2x+6cos(x) ?
The integral of 2x+6cos(x) is x^2+6sin(x)+C