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Levart [38]
2 years ago
15

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

Mathematics
1 answer:
Temka [501]2 years ago
6 0
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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6(3X +5 ) = 7(2x +2)
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Answer:

X=-4 last answer i got i hope it is helpful have a nice day

Step-by-step explanation:

Let's solve your equation step-by-step.

6(3x+5)=7(2x+2)

Step 1: Simplify both sides of the equation.

6(3x+5)=7(2x+2)

(6)(3x)+(6)(5)=(7)(2x)+(7)(2)(Distribute)

18x+30=14x+14

Step 2: Subtract 14x from both sides.

18x+30−14x=14x+14−14x

4x+30=14

Step 3: Subtract 30 from both sides.

4x+30−30=14−30

4x=−16

Step 4: Divide both sides by 4.

4x

4

=

−16

4

x=−4

Answer:

x=−4

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