∫ log(m^2+4m-5)^pi/sin(logpi/2)^cospi eching

$$\int \log \frac { ( m ^ { 2 } + 4 m - 5 ) ^ { \pi } } { \sin ( \log \pi / 2 ) ^ { \cos \pi } }$$

Baholash

$$\log(e)x\left(\pi \ln(\left(m-1\right)\left(m+5\right))+\ln(0,19486506597972128)\right)+С$$

Yechim qadamlari

Evaluate trigonometric functions in the problem

$$\int {\log_{10} {(\frac{{(m ^ {2} + 4 m - 5)} ^ {\pi}}{0,19486506597972128 ^ {\cos(\pi)}})}} dx$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, \log_{10}\left(\frac{\left(m^{2}+4m-5\right)^{\pi }}{0,19486506597972128^{\cos(\pi )}}\right) integralini toping.

$$\log_{10}\left(\frac{\left(m^{2}+4m-5\right)^{\pi }}{0,19486506597972128^{\cos(\pi )}}\right)x$$

Qisqartirish.

$$\frac{\left(\pi \ln(m^{2}+4m-5)+\ln(\frac{608953331186629}{3125000000000000})\right)x}{\ln(10)}$$

Агар F\left(x\right)f\left(x\right) ning dastlabki holati boʻlsa, u holatda f\left(x\right) ning barcha dastlabki holatlari toʻplami F\left(x\right)+C tarafidan belgilanadi. Shu sababli natijaga C\in \mathrm{R} integrallash konstantasini qoʻshing.

$$\frac{\left(\pi \ln(m^{2}+4m-5)+\ln(\frac{608953331186629}{3125000000000000})\right)x}{\ln(10)}+С$$

x ga nisbatan hosilani topish

$$\log(e)\left(\pi \ln(\left(m-1\right)\left(m+5\right))+\ln(0,19486506597972128)\right)$$