∫ ((y+1)^2/x)-এর সমাধান করুন

$$\int ( \frac { ( y + 1 ) ^ { 2 } } { x } )$$

মূল্যায়ন করুন

$$\left(y+1\right)^{2}\ln(|x|)+С$$

সমাধানের ধাপগুলো

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

$$\left(y+1\right)^{2}\int \frac{1}{x}\mathrm{d}x$$

Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.

$$\left(y+1\right)^{2}\ln(|x|)$$

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.

$$\left(y+1\right)^{2}\ln(|x|)+С$$

w.r.t. x পার্থক্য করুন

$$\frac{\left(y+1\right)^{2}}{x}$$