∫ 1/x+x wrt x-এর সমাধান করুন

$$\int \frac { 1 } { x } + x d x$$

মূল্যায়ন করুন

$$\ln(|x|)+\frac{x^{2}}{2}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

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

Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.

$$\ln(|x|)+\int x\mathrm{d}x$$

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}.

$$\ln(|x|)+\frac{x^{2}}{2}$$

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.

$$\ln(|x|)+\frac{x^{2}}{2}+С$$

w.r.t. x পার্থক্য করুন

$$x+\frac{1}{x}$$