∫ (-15x^5+5) wrt x-এর সমাধান করুন

$$\int{ (-15 { x }^{ 5 } +5) }d x$$

মূল্যায়ন করুন

$$-\frac{5x^{6}}{2}+5x+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int -15x^{5}\mathrm{d}x+\int 5\mathrm{d}x$$

Factor out the constant in each of the terms.

$$-15\int x^{5}\mathrm{d}x+\int 5\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{5}\mathrm{d}x with \frac{x^{6}}{6}. -15 কে \frac{x^{6}}{6} বার গুণ করুন।

$$-\frac{5x^{6}}{2}+\int 5\mathrm{d}x$$

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

$$-\frac{5x^{6}}{2}+5x$$

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.

$$-\frac{5x^{6}}{2}+5x+С$$

w.r.t. x পার্থক্য করুন

$$5-15x^{5}$$