∫ x+12y wrt x-এর সমাধান করুন

$$\int{ x+12y }d x$$

মূল্যায়ন করুন

$$12xy+\frac{x^{2}}{2}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int x\mathrm{d}x+\int 12y\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int x\mathrm{d}x+12\int y\mathrm{d}x$$

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}.

$$\frac{x^{2}}{2}+12\int y\mathrm{d}x$$

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

$$\frac{x^{2}}{2}+12yx$$

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.

$$\frac{x^{2}}{2}+12yx+С$$

w.r.t. x পার্থক্য করুন

$$x+12y$$