What is the integral of sqrt(t)-4cos(t) ?

The integral of sqrt(t)-4cos(t) is 2/3 t^{3/2}-4sin(t)+C

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integral of sqrt(t)-4cos(t)

\int t - 4 cos (t) d t

\frac{2}{3} t^{\frac{3}{2}} - 4 sin (t) + C

Solution steps

\int t - 4 cos (t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t d t - \int 4 cos (t) d t

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

\int 4 cos (t) d t = 4 sin (t)

= \frac{2}{3} t^{\frac{3}{2}} - 4 sin (t)

Add a constant to the solution

= \frac{2}{3} t^{\frac{3}{2}} - 4 sin (t) + C

y = x^{3}, at x = 5

\frac{2 r - 1}{t} d r + \frac{r - 2 r ^{2}}{t ^{2} - 1} d t = 0

\frac{d}{d x} (3 x^{4} - 2 x^{3} - 12 x^{2} + 18 x + 15)

g (x) = x + x

2 sin (x), 3 cos (x)

What is the integral of sqrt(t)-4cos(t) ?
The integral of sqrt(t)-4cos(t) is 2/3 t^{3/2}-4sin(t)+C