Question

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

score 252 · Answer 1 · 2026-04-16 09:07:15

252

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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 16 Apr 2026 - 9:07

score 170 · Answer 2 · 2026-04-15 02:31:49

170

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

Published on 15 Apr 2026 - 2:31

score 72 · Answer 3 · 2026-04-15 22:56:53

72

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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 15 Apr 2026 - 22:56

score 236 · Answer 4 · 2026-04-16 05:17:17

236

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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 16 Apr 2026 - 5:17

score 164 · Answer 5 · 2026-04-15 19:37:41

164

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

Published on 15 Apr 2026 - 19:37

score 134 · Answer 6 · 2026-05-10 17:01:52

134

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

Published on 10 May 2026 - 17:01

score 952 · Answer 7 · 2026-04-16 19:40:11

952

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

Published on 16 Apr 2026 - 19:40

score 94 · Answer 8 · 2026-04-13 18:24:32

94

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

Published on 13 Apr 2026 - 18:24

score 138 · Answer 9 · 2026-04-17 04:28:28

138

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

Published on 17 Apr 2026 - 4:28

score 98 · Answer 10 · 2026-04-17 12:54:43

98

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

Published on 17 Apr 2026 - 12:54

score 205 · Answer 11 · 2026-04-09 04:15:32

205

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Integration of powers of trigonometric function with linear term

Published on 09 Apr 2026 - 4:15

score 525 · Answer 12 · 2026-05-11 09:33:36

525

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

Published on 11 May 2026 - 9:33

score 562 · Answer 13 · 2026-04-11 04:22:09

562

Views

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

Published on 11 Apr 2026 - 4:22

score 368 · Answer 14 · 2026-04-15 07:17:38

368

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

Published on 15 Apr 2026 - 7:17

score 334 · Answer 15 · 2026-04-15 21:41:06

334

Views

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

Published on 15 Apr 2026 - 21:41

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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