Which graph g(x)=f(x+2)-5

Mathematics

1 answer:

Vikki [24]3 years ago

4 0

What graph can you add a picture?.

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3 years ago

Giải phương trình y"= lnx

kipiarov [429]

Integrate both sides with respect to <em>x</em> :

$y''(x) = \ln(x) \implies \displaystyle \int y''(x)\,\mathrm dx = \int \ln(x)\,\mathrm dx$

On the right side, integrate by parts with

$f = \ln(x) \implies \mathrm df = \dfrac{\mathrm dx}x \\\\ \mathrm dg = \mathrm dx \implies g = x$

$\implies \displaystyle \int\ln(x)\,\mathrm dx = fg - \int g\,\mathrm df \\\\ \int\ln(x)\,\mathrm dx= x\ln(x) - \int \mathrm dx \\\\ \int\ln(x)\,\mathrm dx= x\ln(x) - x + C_1$

Then

$\displaystyle y'(x) = x\ln(x) - x + C_1$

Integrate both sides with respect to <em>x</em> by parts again, this time with

$f = \ln(x) \implies \mathrm df = \dfrac{\mathrm dx}x \\\\ \mathrm dg = x\,\mathrm dx \implies g = \dfrac{x^2}2$

$\implies \displaystyle \int x\ln(x)\,\mathrm dx = fg-\int g\,\mathrm df \\\\ \int x\ln(x)\,\mathrm dx = \dfrac{x^2\ln(x)}2 - \int\frac x2\,\mathrm dx \\\\ \int x\ln(x)\,\mathrm dx = \dfrac{x^2\ln(x)}2-\dfrac{x^2}4 + C_2$