What is the integral of 2t-3sin(t) ?

The integral of 2t-3sin(t) is t^2+3cos(t)+C

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integral of 2t-3sin(t)

\int 2 t - 3 sin (t) d t

t^{2} + 3 cos (t) + C

Solution steps

\int 2 t - 3 sin (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 2 t d t - \int 3 sin (t) d t

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

\int 3 sin (t) d t = - 3 cos (t)

= t^{2} - (- 3 cos (t))

Simplify

= t^{2} + 3 cos (t)

Add a constant to the solution

= t^{2} + 3 cos (t) + C

\frac{d}{d x} (6 x^{2} - 7 x)

\frac{d y}{d x} = \frac{3 y}{x}

\int x^{- 4} (x + 1) d x

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

\int_{1}^{3} \frac{6}{x} d x

What is the integral of 2t-3sin(t) ?
The integral of 2t-3sin(t) is t^2+3cos(t)+C