∫ (4x^2+2x) wrt x-এর সমাধান করুন

$$\int ( 4 x ^ { 2 } + 2 x ) d x$$

মূল্যায়ন করুন

$$\frac{4x^{3}}{3}+x^{2}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int 4x^{2}\mathrm{d}x+\int 2x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$4\int x^{2}\mathrm{d}x+2\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}. 4 কে \frac{x^{3}}{3} বার গুণ করুন।

$$\frac{4x^{3}}{3}+2\int x\mathrm{d}x$$

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}. 2 কে \frac{x^{2}}{2} বার গুণ করুন।

$$\frac{4x^{3}}{3}+x^{2}$$

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.

$$\frac{4x^{3}}{3}+x^{2}+С$$

w.r.t. x পার্থক্য করুন

$$2x\left(2x+1\right)$$