What is the integral of sqrt(t)-5cos(t) ?

The integral of sqrt(t)-5cos(t) is 2/3 t^{3/2}-5sin(t)+C

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integral of sqrt(t)-5cos(t)

\int t - 5 cos (t) d t

\frac{2}{3} t^{\frac{3}{2}} - 5 sin (t) + C

Solution steps

\int t - 5 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 5 cos (t) d t

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

\int 5 cos (t) d t = 5 sin (t)

= \frac{2}{3} t^{\frac{3}{2}} - 5 sin (t)

Add a constant to the solution

= \frac{2}{3} t^{\frac{3}{2}} - 5 sin (t) + C

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

arcsec (e^{2 x})

\frac{d y}{d x} = 14 x^{8}

\frac{d}{d x} (x \cdot ∣ x ∣)

x \to - 1 lim (x + a)

What is the integral of sqrt(t)-5cos(t) ?
The integral of sqrt(t)-5cos(t) is 2/3 t^{3/2}-5sin(t)+C