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Fluents.

arc tang

da

[ocr errors]

xdx

[ocr errors]
[ocr errors]

f xdx

[ocr errors]

M. xTM(f+gx°)−1(a+bx2)3⁄4dx=x”y—1z3d.x

[ocr errors]

arc tang

ag-bfx
√—(ag2+bf2)√3

3 = / - /

(f+gx)√(a+bx2)

[ocr errors]
[subsumed][ocr errors]

f+gx2 8 •x√(a+bx2)dx

340.

ƒ+gx2

341.

dx

[ocr errors]

331.

[ocr errors]

f2

[ocr errors]
[ocr errors]

(f+gx)√(a+bx2)

[blocks in formation]
[ocr errors][merged small][merged small][subsumed][merged small][merged small]
[blocks in formation]

x*(f+gx)(√a+bx2) xy√z

dr

[ocr errors]
[merged small][ocr errors][ocr errors][merged small]

dx g

dx

=

x2(ƒ+gx)√(a+bx2) x2+z ƒ2

dx

[ocr errors]
[blocks in formation]
[ocr errors]

g2

[ocr errors]

+ $S-$ Sz

+

[ocr errors]
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Putting ag2-bfg+cf2=k

dx

[ocr errors]
[blocks in formation]
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xdx

2ag-bf+(bg-2cf)x+2↓k√%

y
2ag-bf+(bg-2cf)x

arc tang- 2-ky

dx f

[ocr errors]

x2dx

1 xdx f

= = = = - S

f+gx)√(a+bx+cx2) ge
fo dx

[merged small][ocr errors]

+

[ocr errors]
[ocr errors]

f+gx)√(a+bx+cx2)
xdxf2
+

[ocr errors][ocr errors]

dx f3

O. (aa—x1)±3dx.

S

dx

Particular values, from x=0 to x = a.

dx

1

[blocks in formation]

=

[ocr errors]
[blocks in formation]

√(a*—x4)

2a

(f+gx2)√(a+bx2) ̄ √(ag2—bfg)

gz-(ag2-bfg)

[ocr errors]

2

+

[ocr errors]

g2

dr

VOL. IV. PART I.

PP

[merged small][merged small][merged small][merged small][ocr errors][subsumed]
[ocr errors]

1 1.3 1 1 3

[ocr errors]

+

[ocr errors]

2 4 4.6 2.4

[ocr errors]
[ocr errors]
[ocr errors]

1.3. 5

6 4.6.8

[ocr errors][ocr errors]
[ocr errors]
[ocr errors]
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357.

358.

M

B. cosodo

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[ocr errors][merged small]
[ocr errors]

2

[blocks in formation]

359. Scos3pdp = (}}

360.

M

x

1

[ocr errors]

3.14159 M+N

361.

M+1

Cosec

180°

M+N

362.

3

3

= 12 sin 30+ sin

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[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

5

24

sin+16

5

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors]

3

[blocks in formation]
[ocr errors]
[blocks in formation]

15

15

[ocr errors]

6

1

5

80

[ocr errors]

30.

48

8

5

5

24

16

[blocks in formation]
[blocks in formation]

364. Ssino cosqdq=sin*+1¢

We have for the powers of sin ?, sin*4=

[blocks in formation]

5

+16

1

N=4P+2; and sin*Q=±2N=1

sin N

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Fluents.

hl

2

sin+4+1 ) cosp

+2 hl cos

5

[ocr errors]

5

2.

hl

tang (45°+2)

M d. sin cos-dø.

=

3 cos33
sin3

3 cosp

= (sin

=

(

sin20

4

1

= tang34

[ocr errors]

1

3 cos30

sin3p-sin

tang3p-tang +7°

=

=

[merged small][ocr errors][subsumed]
[ocr errors]

1

[ocr errors]

5

(- sin' + 10 sine sine))

3

-

[merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][ocr errors]
[merged small][merged small][ocr errors][merged small][merged small]

seco

431.

[blocks in formation]

sin cos

[blocks in formation]
[blocks in formation]

sin2+2) cosq

1

[ocr errors]
[ocr errors]

=

2

[ocr errors]
[ocr errors]

=cos+seco

3

1

3

2

[blocks in formation]

sin5pdo

1

4

8

[ocr errors]

417.

=

sin40

sin2+

cos2p

3

3

3 cos

[ocr errors][merged small][merged small]

Psin odo. φαφ. 1 cos5 4 cos⭑Q sin2@do cos3

=

(sin34 + 1 sin

8

tang (45 (45° + 2)

sin1 4 cost

[blocks in formation]
[blocks in formation]
[blocks in formation]
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[merged small][ocr errors][merged small]

sin1odo sim

cos p

sinodo cos Q

cos =

1

4

sinRødø

[ocr errors]

Cos

=

3

8

sin3p-sino)+ ht

tang (45°+2)

=

tang p

[blocks in formation]
[blocks in formation]
[ocr errors][merged small]
[merged small][merged small][ocr errors][merged small][merged small]

hl

[blocks in formation]
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