∫ (8x+x^8)-এর সমাধান করুন

$$\int ( 8 x + x ^ { 8 } )$$

মূল্যায়ন করুন

$$\frac{x^{9}}{9}+4x^{2}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int 8x\mathrm{d}x+\int x^{8}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$8\int x\mathrm{d}x+\int x^{8}\mathrm{d}x$$

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}. 8 কে \frac{x^{2}}{2} বার গুণ করুন।

$$4x^{2}+\int x^{8}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{8}\mathrm{d}x with \frac{x^{9}}{9}.

$$4x^{2}+\frac{x^{9}}{9}$$

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.

$$4x^{2}+\frac{x^{9}}{9}+С$$

w.r.t. x পার্থক্য করুন

$$x\left(x^{7}+8\right)$$