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Aneli [31]
2 years ago
14

ate\int log \: x \: dx" alt=" \sf Evaluate\int log \: x \: dx" align="absmiddle" class="latex-formula">
\\  \\  \\  \\  \\  \\  \\  \\  \\ \sjsjsjsj

Thenkewww ☃️


​
Mathematics
2 answers:
Greeley [361]2 years ago
8 0

Answer:

x(log(x) - 1) + C

Step-by-step explanation:

The formula for the derivative of a logarithm function is:

\frac{d}{dx} log_{a}(x)  =  \frac{1}{xlog(a)}

For your case, the base is 10. Now that we have the derivative, lets use integration by parts. I will be differentiating log(x) and integrating 1:

u = log(x)

du = dx/xlog(10)

dv = 1

v = x

You get:

log(x)x - integral(dx/log(10))

Therefore the answer is:

log(x)x - x/log(10) + C

x(log(x) - 1) + C

Georgia [21]2 years ago
6 0

\sf \huge \underline \pink{ \purple {Answer : }}

\:  \:

\:  \:  \:  \:  \:  \:  \:  \rm \large log \: xdx =  \int \: log \: x *\: 1dx

\:

\:  \:  \:  \:  \:  \:  \:  \rm \large = log \: x \int  1 \: dx -  \int \: ( \int \: 1dx \:  \frac{d}{dx} log \: x)dx

\:  \:

\:  \:  \:  \:  \:  \:  \:  \rm \large \:  = x \: log \: x - x + c

\:  \:  \:

\:  \:  \:  \:  \:  \:  \:  \rm \large \:  = log \: x \: (x) -  \int \: x \:  \frac{1}{x} dx

\:  \:

\:  \:  \:  \:  \:  \:  \:  \rm \large = x \: log \: x  - \int \: 1dx

\:  \:

\:  \:  \:  \:  \:  \:  \  \rm \color{red}  \bold{\large = x(log \: x - 1) + c}

\:  \:  \:  \:  \:  \:  \:  \:

\\  \\  \\  \\  \\  \\  \\  \\  \\  \\  \\  \\  \\  \\

Hope Helps!

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