∫ x^2+cosx wrt x-এর সমাধান করুন

$$\int x ^ { 2 } + \cos x d x$$

মূল্যায়ন করুন

$$\sin(x)+\frac{x^{3}}{3}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

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

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}.

$$\frac{x^{3}}{3}+\int \cos(x)\mathrm{d}x$$

Use \int \cos(x)\mathrm{d}x=\sin(x) from the table of common integrals to obtain the result.

$$\frac{x^{3}}{3}+\sin(x)$$

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.

$$\frac{x^{3}}{3}+\sin(x)+С$$

w.r.t. x পার্থক্য করুন

$$\cos(x)+x^{2}$$