∫ (3x^2+x+5) wrt x-এর সমাধান করুন

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

মূল্যায়ন করুন

$$x^{3}+\frac{x^{2}}{2}+5x+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

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

Factor out the constant in each of the terms.

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

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}. 3 কে \frac{x^{3}}{3} বার গুণ করুন।

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

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}.

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

Find the integral of 5 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$x^{3}+\frac{x^{2}}{2}+5x$$

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.

$$x^{3}+\frac{x^{2}}{2}+5x+С$$

w.r.t. x পার্থক্য করুন

$$3x^{2}+x+5$$