Solve ∫ (t^2-sint)dt

$$\int ( t ^ { 2 } - \sin t ) d t$$

Evaluate

$$\cos(t)+\frac{t^{3}}{3}+С$$

Solution Steps

Integrate the sum term by term.

$$\int t^{2}\mathrm{d}t+\int -\sin(t)\mathrm{d}t$$

Factor out the constant in each of the terms.

$$\int t^{2}\mathrm{d}t-\int \sin(t)\mathrm{d}t$$

Since \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} for k\neq -1, replace \int t^{2}\mathrm{d}t with \frac{t^{3}}{3}.

$$\frac{t^{3}}{3}-\int \sin(t)\mathrm{d}t$$

Use \int \sin(t)\mathrm{d}t=-\cos(t) from the table of common integrals to obtain the result. Multiply -1 times -\cos(t).

$$\frac{t^{3}}{3}+\cos(t)$$

If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{t^{3}}{3}+\cos(t)+С$$

Differentiate w.r.t. t

$$-\sin(t)+t^{2}$$