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

The integral of sqrt(2x)-cos(6x) is sqrt(2)xsqrt(x)-(sqrt(2))/3 x^{3/2}-1/6 sin(6x)+C

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integral of sqrt(2x)-cos(6x)

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

2 x x - \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{6} sin (6 x) + C

Solution steps

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

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

\int cos (6 x) d x = \frac{1}{6} sin (6 x)

= 2 x x - \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{6} sin (6 x)

Add a constant to the solution

= 2 x x - \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{6} sin (6 x) + C

(y e^{- 2 x} + y^{3}) d x - e^{- 2 x} d y = 0

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

f (x) = e^{x^{3} + 10 x}

\int 10 x + 2 d x

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

What is the integral of sqrt(2x)-cos(6x) ?
The integral of sqrt(2x)-cos(6x) is sqrt(2)xsqrt(x)-(sqrt(2))/3 x^{3/2}-1/6 sin(6x)+C