Question

Integrate $\frac{x}{\sqrt{1-x^2}}$

score 125 · Answer 1 · 2026-03-30 01:53:09

125

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Integrate $\frac{x}{\sqrt{1-x^2}}$

Published on 30 Mar 2026 - 1:53

score 143 · Answer 2 · 2023-08-23 16:26:17

143

Views

Evaluate the integral: $\int \frac{x^2}{{(a + bx)}^2} \, dx$

Published on 23 Aug 2023 - 16:26

score 197 · Answer 3 · 2023-08-25 06:40:56

197

Views

Evaluate $\int \frac{1}{x \sqrt{16x^2-9}}dx$

Published on 25 Aug 2023 - 6:40

score 195 · Answer 4 · 2023-08-26 11:46:46

195

Views

The integral solved $\int x^{\ln(x)-1}\ln(x)\,\mathrm dx$

Published on 26 Aug 2023 - 11:46

score 69 · Answer 5 · 2026-04-07 19:10:39

69

Views

integration of second order differential equation about SHM

Published on 07 Apr 2026 - 19:10

score 90 · Answer 6 · 2023-08-31 20:46:24

90

Views

Indefinite integral of 0 conflict

Published on 31 Aug 2023 - 20:46

score 72 · Answer 7 · 2023-09-01 05:36:05

72

Views

Help on how I manipulate the algebra when there's a square root

Published on 01 Sep 2023 - 5:36

score 607 · Answer 8 · 2023-09-07 23:57:34

607

Views

complex antiderivative of $\frac{1}{x}$ | why do we put the absolute value in the antiderivative of $\frac{1}{x}= \ln|x|+C $ and not just $\ln(x)+C$

Published on 07 Sep 2023 - 23:57

score 277 · Answer 9 · 2026-04-04 07:36:42

277

Views

Integral Calculus Question: $ g\left(x\right)=\int\frac{x^2-12}{\left(x^2-6x+k^2\right)^2}dx $ where $k \in \Bbb N$

Published on 04 Apr 2026 - 7:36

score 58 · Answer 10 · 2026-04-07 21:18:03

58

Views

Integrate the function (indefinite)

Published on 07 Apr 2026 - 21:18

score 90 · Answer 11 · 2023-09-14 20:00:38

90

Views

$\int \frac{1}{(1-x^2)(2x^2-1)^{\frac{1}{4}}} dx$

Published on 14 Sep 2023 - 20:00

score 168 · Answer 12 · 2026-03-30 01:52:04

168

Views

Verification of solution by $u$-substitution of $\int \frac{\ln x}{1+x^2}dx$

Published on 30 Mar 2026 - 1:52

score 220 · Answer 13 · 2023-09-16 14:36:39

220

Views

Deriving $\int \frac{dz}{z\sqrt{1-z^2}}=\operatorname{Log}(\frac{\tanh(\frac{arcosh(z)}{2})+i}{\tanh(\frac{arcosh(z)}{2})-i})+C$

Published on 16 Sep 2023 - 14:36

score 160 · Answer 14 · 2023-09-16 17:35:56

160

Views

On $\displaystyle\frac{\tanh\left(\frac{\cosh^{-1}(z)}{2}\right)+i}{\tanh\left(\frac{\cosh^{-1}(z)}{2}\right)-i}+C=-\frac{z}{\sqrt{1-{z^2}}+1}$

Published on 16 Sep 2023 - 17:35

score 50 · Answer 15 · 2023-09-16 18:43:12

50

Views

What are the limitations of the product rule(integration by parts) and when to use it?

Published on 16 Sep 2023 - 18:43

List Question

Integrate $\frac{x}{\sqrt{1-x^2}}$

Evaluate the integral: $\int \frac{x^2}{{(a + bx)}^2} \, dx$

Evaluate $\int \frac{1}{x \sqrt{16x^2-9}}dx$

The integral solved $\int x^{\ln(x)-1}\ln(x)\,\mathrm dx$

integration of second order differential equation about SHM

Indefinite integral of 0 conflict

Help on how I manipulate the algebra when there's a square root

complex antiderivative of $\frac{1}{x}$ | why do we put the absolute value in the antiderivative of $\frac{1}{x}= \ln|x|+C $ and not just $\ln(x)+C$

Integral Calculus Question: $ g\left(x\right)=\int\frac{x^2-12}{\left(x^2-6x+k^2\right)^2}dx $ where $k \in \Bbb N$

Integrate the function (indefinite)

$\int \frac{1}{(1-x^2)(2x^2-1)^{\frac{1}{4}}} dx$

Verification of solution by $u$-substitution of $\int \frac{\ln x}{1+x^2}dx$

Deriving $\int \frac{dz}{z\sqrt{1-z^2}}=\operatorname{Log}(\frac{\tanh(\frac{arcosh(z)}{2})+i}{\tanh(\frac{arcosh(z)}{2})-i})+C$

On $\displaystyle\frac{\tanh\left(\frac{\cosh^{-1}(z)}{2}\right)+i}{\tanh\left(\frac{\cosh^{-1}(z)}{2}\right)-i}+C=-\frac{z}{\sqrt{1-{z^2}}+1}$

What are the limitations of the product rule(integration by parts) and when to use it?

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