Mathematics: How do you integrate arctan(x dx? i think that if you simplify the integral you get: ?

How do you integrate arctan(x dx? i think that if

Ответ:

VETORRES

02.01.2022

Integration by parts will help here. Letting $u=\arctan x$ and $\mathrm dv=\mathrm dx$ , you end up with $\mathrm du=\dfrac{\mathrm dx}{1+x^2}$ and v=x

. Now

$\displaystyle\int\arctan x\,\mathrm dx=uv-\int v\,\mathrm du$
$\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\int\frac x{1+x^2}\,\mathrm dx$

For the remaining integral, setting y=1+x^2

gives $\dfrac{\mathrm dy}2=x\,\mathrm dx$ , so

$\displaystyle\int\frac x{1+x^2}\,\mathrm dx=\frac12\int\frac{\mathrm dy}y=\frac12\ln|y|+C=\frac12\ln(1+x^2)+C$

Putting everything together, you end up with

$\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\frac12\ln(1+x^2)+C$

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Ответ:

dunayahsu

27.03.2021

Mathematics

t = 1 1/4 hours

Step-by-step explanation:

Lets first make an equation to represent the situation. t + 1/2 = 1 3/4

Because we cant add fractions with different denominators we have to change 1/2 to 2/4.

Next, we need to isolate t. Subtract 2/4 from both sides of the equation to get 1 1/4.

t = 1 1/4.

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How do you integrate arctan(x dx? i think that if you simplify the integral you get: ?

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