List questions from trigonometric-integrals

Published on 17 Apr 2026 - 6:54

120

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Why does $\frac{\sin x}{x}$ have no anti-derivative

Published on 16 Apr 2026 - 20:18

150

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How to calculate the integral $\int \frac{a\tan^2{x}+b}{a^2\tan^2{x}+b^2} dx$?

Published on 14 Apr 2026 - 9:59

184

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How to evaluate $\int\frac{ \sin^8 x - \cos^8x } { 1 - 2\sin^2 x \cdot \cos^2 x }\mathrm{d}x$?

Published on 15 Apr 2026 - 21:44

126

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$I_n = \int_{0}^{\frac{\pi}{2}}(\cos t)^n \ dt$ converges to 0?

Published on 14 Apr 2026 - 22:24

157

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Evaluate: $ \int \frac{\sin x}{\sin x - \cos x} dx $

Published on 15 Apr 2026 - 17:46

1.8k

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How can I solve $\int_0^1\frac{\arctan(x^2)}{1+x^2}\,\mathrm dx$?

Published on 16 Apr 2026 - 9:34

238

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A different method of evaluating $ \int\frac{1}{\sqrt{\sin^3(x)\cdot\sin(x+\alpha})}\,dx$

Published on 16 Apr 2026 - 1:08

749

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How to integrate $ \int \frac{\sin {3x} + \cos{3x}}{ \sin^3 x + \cos^3 x } dx\ $

Published on 15 Apr 2026 - 14:34

289

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Contour Integral of irrational polynomial from -1 to 1

Published on 15 Apr 2026 - 21:23

31

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Trigonometric Substiution

Published on 13 Apr 2026 - 15:56

148

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Finding $\int \sin^5(2x)\cos^3(3x)~dx$

Published on 15 Apr 2026 - 21:14

159

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How to integrate $\int_{1}^{e} (x+1)e^{x}\ln{x}dx $?

Published on 14 Apr 2026 - 17:50

328

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Calculating $\int_0^{\pi/2} \frac{\ln(\sin x+\cos x)}{\sin x\cos x}\, dx$

Published on 15 Apr 2026 - 20:25

132

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Evaluating $\int_{-\infty}^\infty e^{i(ax^2+bx+c)}\frac{\operatorname{sin}^2x}{x^2}dx$

Published on 15 Apr 2026 - 8:06

List Question

Integrate $\int_0^1 \sin^{-1}{\frac{x^2}{1+x^2}}dx$

Why does $\frac{\sin x}{x}$ have no anti-derivative

How to calculate the integral $\int \frac{a\tan^2{x}+b}{a^2\tan^2{x}+b^2} dx$?

How to evaluate $\int\frac{ \sin^8 x - \cos^8x } { 1 - 2\sin^2 x \cdot \cos^2 x }\mathrm{d}x$?

$I_n = \int_{0}^{\frac{\pi}{2}}(\cos t)^n \ dt$ converges to 0?

Evaluate: $ \int \frac{\sin x}{\sin x - \cos x} dx $

How can I solve $\int_0^1\frac{\arctan(x^2)}{1+x^2}\,\mathrm dx$?

A different method of evaluating $ \int\frac{1}{\sqrt{\sin^3(x)\cdot\sin(x+\alpha})}\,dx$

How to integrate $ \int \frac{\sin {3x} + \cos{3x}}{ \sin^3 x + \cos^3 x } dx\ $

Contour Integral of irrational polynomial from -1 to 1

Trigonometric Substiution

Finding $\int \sin^5(2x)\cos^3(3x)~dx$

How to integrate $\int_{1}^{e} (x+1)e^{x}\ln{x}dx $?

Calculating $\int_0^{\pi/2} \frac{\ln(\sin x+\cos x)}{\sin x\cos x}\, dx$

Evaluating $\int_{-\infty}^\infty e^{i(ax^2+bx+c)}\frac{\operatorname{sin}^2x}{x^2}dx$

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