∫ 2^x/9e^4+4 wrt x-এর সমাধান করুন

$$\int \frac { 2 ^ { x } } { 9 e ^ { 4 } + 4 } d x$$

মূল্যায়ন করুন

$$\frac{2^{x}}{\left(9e^{4}+4\right)\ln(2)}+С$$

সমাধানের ধাপগুলো

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{\int 2^{x}\mathrm{d}x}{9e^{4}+4}$$

Use \int p^{q}\mathrm{d}q=\frac{p^{q}}{\ln(p)} from the table of common integrals to obtain the result.

$$\frac{2^{x}}{\ln(2)\left(9e^{4}+4\right)}$$

সিমপ্লিফাই।

$$\frac{2^{x}}{\left(9e^{4}+4\right)\ln(2)}$$

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.

$$\frac{2^{x}}{\left(9e^{4}+4\right)\ln(2)}+С$$

w.r.t. x পার্থক্য করুন

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