∫ 2x^5+3x wrt x-এর সমাধান করুন

$$\int 2 x ^ { 5 } + 3 x d x$$

মূল্যায়ন করুন

$$\frac{x^{6}}{3}+\frac{3x^{2}}{2}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int 2x^{5}\mathrm{d}x+\int 3x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$2\int x^{5}\mathrm{d}x+3\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{5}\mathrm{d}x with \frac{x^{6}}{6}. 2 কে \frac{x^{6}}{6} বার গুণ করুন।

$$\frac{x^{6}}{3}+3\int x\mathrm{d}x$$

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}. 3 কে \frac{x^{2}}{2} বার গুণ করুন।

$$\frac{x^{6}}{3}+\frac{3x^{2}}{2}$$

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.

$$\frac{x^{6}}{3}+\frac{3x^{2}}{2}+С$$

w.r.t. x পার্থক্য করুন

$$x\left(2x^{4}+3\right)$$