Integration (1 Viewer)

tOnnyAyye · Oct 8, 2011

How do you integrate ln(x+1) ?

Amogh · Oct 8, 2011

Well outside the 2-Unit course!

SpiralFlex · Oct 8, 2011

Use integration by parts.

$\int 1*\ln(x+1)\: {\mathrm{d} x}$

$u=\ln(x+1)$

$u'=\frac{1}{x+1}$

$v'=1$

$v=x$

$=x\ln(x+1)-\int \frac{x}{x+1}\: {\mathrm{d} x}$

$=x\ln(x+1)-\int \frac{x+1-1}{x+1}\: {\mathrm{d} x}$

$=x\ln(x+1)-\int (1-\frac{1}{x+1})\: {\mathrm{d} x}$

$=x\ln(x+1)-x+\ln(x+1)+C$

$=(x+1)\ln(x+1)-x+C$

Politic · Oct 8, 2011

SpiralFlex said:
Use integration by parts.

$\int 1*\ln(x+1)dx$

$u=\ln(x+1)$

$u'=\frac{1}{x+1}$

$v'=1$

$v=x$

$=x\ln(x+1)-\int \frac{x}{x+1}dx$

$=x\ln(x+1)-\int \frac{x+1-1}{x+1}dx$

$=x\ln(x+1)-\int (1-\frac{1}{x+1})dx$

$=x\ln(x+1)-x+ln(x+1)$

$=(x+1)\ln(x+1)-x+C$

That's 3U.. this question should be moved to the 3U threads..

SpiralFlex · Oct 8, 2011

politic said:
that's 3u.. This question should be moved to the 3u threads..

4 Unit.

krnofdrg · Oct 8, 2011

tOnnyAyye said:
How do you integrate ln(x+1) ?

you cannot integrate loge or ln remember

... So there should be a method for 2u.. I don't think this is 2u?

D94 · Oct 8, 2011

Politic said:
That's 3U.. this question should be moved to the 3U threads..

IBP is technically 4unit. If the OP is asking this as a 2u question, then the best method is to integrate with respect to the y-axis and then subtract that value from the square/rectangle it makes since we're integrating above the curve.

2/3 Unit Method:
$\\y =ln(x) \\e^{y}=x+1 \\x=e^{y}-1 \\\int e^{y}-1\,dy \\ \\=e^{y} -y + c \\=(x+1)- ln(x+1) + c \\ \\$Now, this is the area with respect to the y axis, so we need to subtract this from the area of a rectangle made by the arbitrary point on the curve, so we can find the area under the curve.$ \\ \\Arbitrary\ Point: P(x,ln(x+1)) \\\therefore Area = xln(x+1) \\\therefore xln(x+1) - ((x+1)- ln(x+1) + c) \\=(x+1)ln(x+1)-x\(-1+c) \\=(x+1)ln(x+1)-x+C$

krnofdrg said:
you cannot integrate loge or ln remember ... So there should be a method for 2u.. I don't think this is 2u?

You can, using integration by parts method.

Integration (1 Viewer)

tOnnyAyye

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Amogh

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SpiralFlex

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Politic

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SpiralFlex

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krnofdrg

Mq Law Student :)

D94

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