HELP ITS DUE IN A FEW MINS WITH MY OTHER QUESTION BUT I NEED MY LAST HELP PLS AND TYYY I WOULD APPRECIATE IT SM <3

Mathematics

1 answer:

kolbaska11 [484]2 years ago

6 0

Answer:

y=3/4x+1

Step-by-step explanation:

up 3 right 4. U better hurry up and answer that question my guy!

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Write a conditional that multiplies the value of the variable pay by one-and-a-half if the value of the boolean variable workedo

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3 years ago

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

Temka [501]

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

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