Question

Evaluate
$f( {x}^{3} - \: \frac{1}{x} + 3x) \: dx$
Please help me with this question​

Answer 1

Answer:

1. For each part, find dy/dx.

(a) y =

3x

3 + 2x

2

√

x

Answer: dy

dx =

15

2

x

3/2 + 3x

1/2

(b) y = xe2x

Answer: dy

dx = (2x + 1)e

2x

(c) y =

1

2

sin (−2x)

Answer: dy

dx = − cos (−2x)

(d) xy = x

2 + y

2

Answer: dy

dx =

2x−y

x−2y

(e) y =

Z x

3

e

−t

2

dt

Answer: dy

dx = e

−x

2

(f) y = (−5x + 2)4

Answer: dy

dx = −20(−5x + 2)3

(g) y =

R 2

x

3 sin (t

2

) dt.

Answer: −3 sin (x

2

)

(h) d

dx [π

e + 2]

Answer: 0. It’s just the derivative of some complicated constant.

(i) d

dx

-

3

x + x

3

Answer: 3

x

ln 3 + 3x

2

(j) d

dt [arctan(t) ln(t/5)]

Answer: ln (t/5)

1 + t

2

+

arctan t

t

(k) d

by r

y + 1

y + 7

Answer: 3

r

y + 7

y + 1

1

(y + 7)2

(l) Let y =

Z x

3

2x

8

ln (4t)

dt, for x > 0.

Answer:

by

dx =

8 · 3x

2

ln(4x

3

)

−

8 · 2

ln(4 · 2x)

Step-by-step explanation:

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