Question

Evaluate $\int x^2\ln (1+x)dx$ as a power series.

score 848 · Answer 1 · 2026-04-03 06:58:32

848

Views

Evaluate $\int x^2\ln (1+x)dx$ as a power series.

Published on 03 Apr 2026 - 6:58

score 1.1k · Answer 2 · 2019-11-09 04:51:03

1.1k

Views

Evaluate $\int x^2\ln (1+x) \, dx$ as a power series: why is just $n$ ok?

Published on 09 Nov 2019 - 4:51

score 29 · Answer 3 · 2019-11-09 05:52:21

29

Views

Find the series having sum equal to x and product equal to y

Published on 09 Nov 2019 - 5:52

score 197 · Answer 4 · 2019-11-09 12:52:53

197

Views

Series expansion of $e^{sinx}$ and set partition

Published on 09 Nov 2019 - 12:52

score 81 · Answer 5 · 2019-11-09 14:47:05

81

Views

Find the radius of convergence of the series $ \sum_{k=1}^{\infty}\left(\frac{x}{\sin k}\right)^k $

Published on 09 Nov 2019 - 14:47

score 71 · Answer 6 · 2019-11-09 16:05:14

71

Views

Why these series have the same radius of convergence?

Published on 09 Nov 2019 - 16:05

score 997 · Answer 7 · 2019-11-09 18:11:28

997

Views

Series expansion for $e^{\sin x}$ and coefficient comparison

Published on 09 Nov 2019 - 18:11

score 285 · Answer 8 · 2026-03-28 03:52:54

285

Views

Laurent expansion of $\sin(z)$ at infinity.

Published on 28 Mar 2026 - 3:52

score 181 · Answer 9 · 2019-11-10 02:20:45

181

Views

Alternative method for expanding $\dfrac{1}{1+\sin(x)}$

Published on 10 Nov 2019 - 2:20

score 47 · Answer 10 · 2019-11-10 10:50:59

47

Views

How do I make the power series of $4x^2y''(x)-4x^2y'(x) + (1-2x)y(x)=0$

Published on 10 Nov 2019 - 10:50

score 386 · Answer 11 · 2026-03-26 17:32:22

386

Views

A power series is real analytic on its radius of convergence.

Published on 26 Mar 2026 - 17:32

score 79 · Answer 12 · 2019-11-10 19:39:15

79

Views

General formula for $e^x+\cos(x)$, $e^x+\sin(x)$, $e^x-\sin(x)$, $e^x-\sin(x)$

Published on 10 Nov 2019 - 19:39

score 62 · Answer 13 · 2026-03-31 23:25:16

62

Views

Double exponential generating function

Published on 31 Mar 2026 - 23:25

score 40 · Answer 14 · 2019-11-11 02:45:48

40

Views

Why must the power series for the derivative of this be shifted over one unit?

Published on 11 Nov 2019 - 2:45

score 121 · Answer 15 · 2026-03-26 01:12:03

121

Views

Is there any generic way to obtain $\sum_{n=0}^\infty \frac{1}{(kn+q)^s}$ from Riemann zeta function?

Published on 26 Mar 2026 - 1:12

List Question

Evaluate $\int x^2\ln (1+x)dx$ as a power series.

Evaluate $\int x^2\ln (1+x) \, dx$ as a power series: why is just $n$ ok?

Find the series having sum equal to x and product equal to y

Series expansion of $e^{sinx}$ and set partition

Find the radius of convergence of the series $ \sum_{k=1}^{\infty}\left(\frac{x}{\sin k}\right)^k $

Why these series have the same radius of convergence?

Series expansion for $e^{\sin x}$ and coefficient comparison

Laurent expansion of $\sin(z)$ at infinity.

Alternative method for expanding $\dfrac{1}{1+\sin(x)}$

How do I make the power series of $4x^2y''(x)-4x^2y'(x) + (1-2x)y(x)=0$

A power series is real analytic on its radius of convergence.

General formula for $e^x+\cos(x)$, $e^x+\sin(x)$, $e^x-\sin(x)$, $e^x-\sin(x)$

Double exponential generating function

Why must the power series for the derivative of this be shifted over one unit?

Is there any generic way to obtain $\sum_{n=0}^\infty \frac{1}{(kn+q)^s}$ from Riemann zeta function?

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