∫ 4+5tdt-এর সমাধান করুন

$$\int 4 + 5 t d t$$

মূল্যায়ন করুন

$$\frac{5t^{2}}{2}+4t+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int 4\mathrm{d}t+\int 5t\mathrm{d}t$$

Factor out the constant in each of the terms.

$$\int 4\mathrm{d}t+5\int t\mathrm{d}t$$

Find the integral of 4 using the table of common integrals rule \int a\mathrm{d}t=at.

$$4t+5\int t\mathrm{d}t$$

Since \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} for k\neq -1, replace \int t\mathrm{d}t with \frac{t^{2}}{2}. 5 কে \frac{t^{2}}{2} বার গুণ করুন।

$$4t+\frac{5t^{2}}{2}$$

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.

$$4t+\frac{5t^{2}}{2}+С$$

w.r.t. t পার্থক্য করুন

$$5t+4$$