∫ (x^5-7+4/x^2) wrt x-এর সমাধান করুন

$$\int ( x ^ { 5 } - 7 + \frac { 4 } { x ^ { 2 } } ) d x$$

মূল্যায়ন করুন

$$\frac{x^{6}}{6}-7x-\frac{4}{x}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int x^{5}\mathrm{d}x+\int -7\mathrm{d}x+\int \frac{4}{x^{2}}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int x^{5}\mathrm{d}x+\int -7\mathrm{d}x+4\int \frac{1}{x^{2}}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{5}\mathrm{d}x with \frac{x^{6}}{6}.

$$\frac{x^{6}}{6}+\int -7\mathrm{d}x+4\int \frac{1}{x^{2}}\mathrm{d}x$$

Find the integral of -7 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x^{6}}{6}-7x+4\int \frac{1}{x^{2}}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{2}}\mathrm{d}x with -\frac{1}{x}. 4 কে -\frac{1}{x} বার গুণ করুন।

$$\frac{x^{6}}{6}-7x-\frac{4}{x}$$

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.

$$\frac{x^{6}}{6}-7x-\frac{4}{x}+С$$

w.r.t. x পার্থক্য করুন

$$x^{5}-7+\frac{4}{x^{2}}$$