∫ x-1 wrt x-এর সমাধান করুন

$$\int x - 1 d x$$

মূল্যায়ন করুন

$$\frac{x^{2}}{2}-x+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int x\mathrm{d}x+\int -1\mathrm{d}x$$

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

$$\frac{x^{2}}{2}+\int -1\mathrm{d}x$$

Find the integral of -1 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x^{2}}{2}-x$$

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

$$\frac{x^{2}}{2}-x+С$$

w.r.t. x পার্থক্য করুন

$$x-1$$