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

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

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

\int x - 6 cos (x) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{x ^{n}}{1 0 ^{n}}

\int_{0}^{1} 36 t^{2} + 9 t^{4} d t

y^{^{'}} = \frac{sin ( 2 x )}{e ^{y}}

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{2} + 1})

\int e^{x} cos (4 y) d x

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