∫ (-4x^5-5) wrt x-এর সমাধান করুন

$$\int ( - 4 x ^ { 5 } - 5 ) d x$$

মূল্যায়ন করুন

$$-\frac{2x^{6}}{3}-5x+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int -4x^{5}\mathrm{d}x+\int -5\mathrm{d}x$$

Factor out the constant in each of the terms.

$$-4\int x^{5}\mathrm{d}x+\int -5\mathrm{d}x$$

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}. -4 কে \frac{x^{6}}{6} বার গুণ করুন।

$$-\frac{2x^{6}}{3}+\int -5\mathrm{d}x$$

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

$$-\frac{2x^{6}}{3}-5x$$

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.

$$-\frac{2x^{6}}{3}-5x+С$$

w.r.t. x পার্থক্য করুন

$$-4x^{5}-5$$