∫ (from -9 to 45) of 5x+8585+68*{(e)^15 wrt x-এর সমাধান করুন

$$\int_{ -9 }^{ 45 } 5x+8585+68 \times {(e)^{ 15 }} d x$$

মূল্যায়ন করুন

$$3672e^{15}+468450\approx 12004300241.717580795$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 5x+8585+68e^{15}\mathrm{d}x$$

Integrate the sum term by term.

$$\int 5x\mathrm{d}x+\int 8585\mathrm{d}x+\int 68e^{15}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$5\int x\mathrm{d}x+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

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}. 5 কে \frac{x^{2}}{2} বার গুণ করুন।

$$\frac{5x^{2}}{2}+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

Find the integral of 8585 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{5x^{2}}{2}+8585x+68\int e^{15}\mathrm{d}x$$

Find the integral of e^{15} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{5x^{2}}{2}+8585x+68e^{15}x$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\frac{5}{2}\times 45^{2}+8585\times 45+68e^{15}\times 45-\left(\frac{5}{2}\left(-9\right)^{2}+8585\left(-9\right)+68e^{15}\left(-9\right)\right)$$

সিমপ্লিফাই।

$$468450+3672e^{15}$$