Question

Integrating $\int \sec xdx$: Why is $\ln|\text{sec}x + \text{tan}x| + C$ preferred over $\tanh^{-1}(\sin x) + C$?

score 250 · Answer 1 · 2026-03-27 05:38:19

250

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Integrating $\int \sec xdx$: Why is $\ln|\text{sec}x + \text{tan}x| + C$ preferred over $\tanh^{-1}(\sin x) + C$?

Published on 27 Mar 2026 - 5:38

score 167 · Answer 2 · 2018-12-12 17:35:25

167

Views

Integral of $\int\frac{\sin x}{\sin x+\cos x}dx$

Published on 12 Dec 2018 - 17:35

score 71 · Answer 3 · 2026-03-26 22:16:10

71

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Why $\int_0^{2\pi} \sin^2 x \mathrm{d}x \neq \int_0^{2\pi}\sin x \sin nx \mathrm{d}x \to n=1$

Published on 26 Mar 2026 - 22:16

score 234 · Answer 4 · 2026-03-27 05:41:59

234

Views

Evaluating $ \int \frac1{5S_{8} - 9S_{10} + 7S_{12} - 2S_{14}} {\rm d}x$, where $S_n = \sin^n(x) + \cos^n(x)$

Published on 27 Mar 2026 - 5:41

score 162 · Answer 5 · 2026-03-27 07:13:39

162

Views

Evaluating $\int \frac{\cos x}{\sin^3x+\sin x}dx$

Published on 27 Mar 2026 - 7:13

score 131 · Answer 6 · 2026-03-25 20:12:00

131

Views

$\int\limits_{0}^{2\pi}[\int\limits_{0}^{\pi}\sin^3\theta \cos^2\{r(\sin \theta \sin \alpha\cos \phi+\cos \theta\cos \alpha)+c\}d\theta] d \phi$

Published on 25 Mar 2026 - 20:12

score 949 · Answer 7 · 2018-12-28 13:48:34

949

Views

A Difficult Definite Integral $\int_0^{2\pi}(t-\sin t)(1-\cos t)^2{\rm d}t.$

Published on 28 Dec 2018 - 13:48

score 92 · Answer 8 · 2026-03-26 03:11:22

92

Views

Is there any solution (numeric or closed) to integration of ${\sin x}^{\cos x}$?

Published on 26 Mar 2026 - 3:11

score 135 · Answer 9 · 2019-01-02 14:10:57

135

Views

Prove $\int_0^\infty\operatorname{sech} x\,dx=\pi/2$, and deduce $\int_0^1\operatorname{sech}^{-1}x\,dx$

Published on 02 Jan 2019 - 14:10

score 97 · Answer 10 · 2026-03-26 04:52:23

97

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$ \int \bigl| a\sin(x)+b\cos(x) \bigr| {\rm d}x = ? $

Published on 26 Mar 2026 - 4:52

score 203 · Answer 11 · 2026-03-27 10:15:47

203

Views

Integration of powers of trigonometric function with linear term

Published on 27 Mar 2026 - 10:15

score 523 · Answer 12 · 2026-03-25 15:17:48

523

Views

Solving $\int_0^{\frac{\pi}{2}}\frac{1}{\sin^{2n}(x) + \cos^{2n}(x)}\:dx$

Published on 25 Mar 2026 - 15:17

score 560 · Answer 13 · 2026-03-27 10:08:18

560

Views

Integral of $\sec(x)$ using $u$ sub

Published on 27 Mar 2026 - 10:08

score 365 · Answer 14 · 2019-01-05 15:24:43

365

Views

What is the solution for $\int_{0}^{\pi/2}\frac{\cos^2x}{\cos^2x+4\sin^2x}\,dx$

Published on 05 Jan 2019 - 15:24

score 331 · Answer 15 · 2019-01-05 21:24:19

331

Views

Don't understand how to use trig sub on $\int\frac{x^3}{(4x^2+9)^\frac{3}{2}}dx$

Published on 05 Jan 2019 - 21:24

List Question

Integrating $\int \sec xdx$: Why is $\ln|\text{sec}x + \text{tan}x| + C$ preferred over $\tanh^{-1}(\sin x) + C$?

Integral of $\int\frac{\sin x}{\sin x+\cos x}dx$

Why $\int_0^{2\pi} \sin^2 x \mathrm{d}x \neq \int_0^{2\pi}\sin x \sin nx \mathrm{d}x \to n=1$

Evaluating $ \int \frac1{5S_{8} - 9S_{10} + 7S_{12} - 2S_{14}} {\rm d}x$, where $S_n = \sin^n(x) + \cos^n(x)$

Evaluating $\int \frac{\cos x}{\sin^3x+\sin x}dx$

$\int\limits_{0}^{2\pi}[\int\limits_{0}^{\pi}\sin^3\theta \cos^2\{r(\sin \theta \sin \alpha\cos \phi+\cos \theta\cos \alpha)+c\}d\theta] d \phi$

A Difficult Definite Integral $\int_0^{2\pi}(t-\sin t)(1-\cos t)^2{\rm d}t.$

Is there any solution (numeric or closed) to integration of ${\sin x}^{\cos x}$?

Prove $\int_0^\infty\operatorname{sech} x\,dx=\pi/2$, and deduce $\int_0^1\operatorname{sech}^{-1}x\,dx$

$ \int \bigl| a\sin(x)+b\cos(x) \bigr| {\rm d}x = ? $

Integration of powers of trigonometric function with linear term

Solving $\int_0^{\frac{\pi}{2}}\frac{1}{\sin^{2n}(x) + \cos^{2n}(x)}\:dx$

Integral of $\sec(x)$ using $u$ sub

What is the solution for $\int_{0}^{\pi/2}\frac{\cos^2x}{\cos^2x+4\sin^2x}\,dx$

Don't understand how to use trig sub on $\int\frac{x^3}{(4x^2+9)^\frac{3}{2}}dx$

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