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PSYCHO15rus [73]

3 years ago

7

FOR BRAINLIEST PLEASE HURRY

2 answers:

julia-pushkina [17]3 years ago

8 0

Answer:

ummm what's the question

Step-by-step explanation:

Nookie1986 [14]3 years ago

5 0

Answer:

Answer:

Step-by-step explanation:

Have a nice day!

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Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t

Anika [276]

Answer:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

Step-by-step explanation:

Given

$\int\limits {\frac{x}{x^4 + 16}} \, dx$

Required

Solve

Let

$u = \frac{x^2}{4}$

Differentiate

$du = 2 * \frac{x^{2-1}}{4}\ dx$

$du = 2 * \frac{x}{4}\ dx$

$du = \frac{x}{2}\ dx$

Make dx the subject

$dx = \frac{2}{x}\ du$

The given integral becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

Recall that: $u = \frac{x^2}{4}$

Make $x^2$ the subject

$x^2= 4u$

Square both sides

$x^4= (4u)^2$

$x^4= 16u^2$

Substitute $16u^2$ for $x^4$ in $\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du$

Simplify

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

In standard integration

$\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)$

So, the expression becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)$

Recall that: $u = \frac{x^2}{4}$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

4 0

3 years ago

Rename 0.600 as place values

Vlad1618 [11]

0.600 = six thousandths written out

5 0

3 years ago

Please help me idk this

Sergio [31]

First take the fractions and find their common denominator:
$\frac{1}{2}$ x 4 = $\frac{4}{8}$

Now you can add the fractions:
$\frac{4}{8} + \frac{1}{8} = \frac{5}{8}$

Now add your whole numbers and the fraction:
1+1= 2 >> 2+ $\frac{5}{8}$ = 2 $\frac{5}{8}$ yards

Now subract 2 $\frac{5}{8}$ from 5:
5-2 $\frac{5}{8}$ =2 $\frac{3}{8}$ yards

4 0

3 years ago

Read 2 more answers

15y+31=61 how do I solve this

Setler79 [48]

15y + 31 = 61
15y = 61 - 31
15y = 30
y = 30 ÷ 15
<u>y = 2</u>

6 0

3 years ago

A: What is the smallest increment on the voltmeter

oee [108]

Answer:

RESOLUTION

Step-by-step explanation:

Resolution is the smallest increment a tool can detect and display. For a nonelectrical example, consider two rulers.

4 0

3 years ago