Resol ∫ sin2x/16-sin^4x wrt x | Microsoft Math Solver

Calcula

-\frac{\ln(\frac{|\left(\sin(x)\right)^{2}-4|}{\left(\sin(x)\right)^{2}+4})}{8}+С

Diferencieu x

-\frac{\sin(2x)\left(\left(\sin(x)\right)^{2}sign(\left(\sin(x)\right)^{2}-4)+4sign(\left(\sin(x)\right)^{2}-4)-|\left(\sin(x)\right)^{2}-4|\right)}{8|\left(\sin(x)\right)^{2}-4|\left(\left(\sin(x)\right)^{2}+4\right)}

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Integration

5 problemes similars a:

\int \frac { \sin 2 x } { 16 - \sin ^ { 4 } x } d x

Problemes similars de la cerca web

What is \displaystyle\int\frac{{\sin{{x}}}}{{{1}-{{\sin}^{{2}}{x}}}}{\left.{d}{x}\right.} ?

https://socratic.org/questions/what-is-int-sin-x-1-sin-2x-dx

\displaystyle{1}-{{\sin}^{{2}}{x}}={{\cos}^{{2}}{x}} and \displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left({\cos{{x}}}\right)}=-{\sin{{x}}} Explanation: Rewrite as \displaystyle\int\frac{{\sin{{x}}}}{{{1}-{{\sin}^{{2}}{x}}}}{\left.{d}{x}\right.}=\int\frac{{\sin{{x}}}}{{{\cos}^{{2}}{x}}}{\left.{d}{x}\right.} ...

How to evaluate \displaystyle\int_0^{\frac{\pi}{4}} \frac{\sin x}{1+x^2} \, \mathrm{d}x

https://www.quora.com/How-do-I-evaluate-displaystyle-int_0-frac-pi-4-frac-sin-x-1%2Bx-2-mathrm-d-x

If you have tried hard with the integral, and you haven't yet found the answer. It is possible that there is no 'nice' expression corresponding to it. One of the way I would check to avoid wasting my ...

Evaluate \int\frac{\sin(8x)}{9+\sin^4(4x)}\,\mathrm dx

https://math.stackexchange.com/questions/1070213/evaluate-int-frac-sin8x9-sin44x-mathrm-dx

Hint : If u = \dfrac{1}{3}\sin^2(4x), then \dfrac{du}{dx} = \dfrac{1}{3} \cdot 2 \cdot \sin(4x) \cdot \cos(4x) \cdot 4 = \dfrac{8}{3}\sin(4x)\cos(4x). Now apply the double angle formula 2\sin\theta\cos\theta = \sin 2\theta ...

What is the integral of \displaystyle\int \dfrac{x \sin x}{x^2+w^2}\,dx ?

https://www.quora.com/What-is-the-integral-of-displaystyle-int-dfrac-x-sin-x-x-2+w-2-dx

Easily done :) \begin{align}I&=\int\dfrac{x\sin x}{x^2+w^2}\mathrm dx\\&=\int\left[\dfrac{x}{(x+iw)(x-iw)}\right]\sin x\,\mathrm dx\\&=\int\left[\dfrac{(x+iw)+(x-iw)}{2(x+iw)(x-iw)}\right]\sin x\,\mathrm dx\\&=\int\dfrac{\sin x}{2(x-iw)}\mathrm dx-\int\dfrac{\sin x}{2(x+iw)}\mathrm dx\\\hline&\text{Let }u=x-iw\implies \mathrm du=\mathrm dx\\&\text{Let }v=x+iw\implies \mathrm dv=\mathrm dx\\\hline&=\int\dfrac{\sin(u+iw)}{2u}\mathrm du-\int\dfrac{\sin(v-iw)}{2v}\mathrm dv\\&=\int\dfrac{\sin u\cos(iw)+\cos u\sin(iw)}{2u}\mathrm du-\int\dfrac{\sin v\cos(iw)-\cos v\sin(iw)}{2v}\mathrm dv\\&=\int\dfrac{\sin u\cosh w+i\cos u\sinh w}{2u}\mathrm du-\int\dfrac{\sin v\cosh w-i\cos v\sinh w}{2v}\mathrm dv\\&=\dfrac12\cosh w\int\dfrac{\sin u}u\mathrm du+\dfrac12i\sinh w\int\dfrac{\cos u}u\mathrm du-\dfrac12\cosh w\int\dfrac{\sin v}v\mathrm dv+\dfrac12i\sinh w\int\dfrac{\cos v}v\mathrm dv\\&=\dfrac12\cosh(w)\mathrm{Si}(u)+\dfrac12i\sinh(w)\mathrm{Ci}(u)-\dfrac12\cosh(w)\mathrm{Si}(v)+\dfrac12i\sinh(w)\mathrm{Ci}(v)+C\\&=\boxed{\boxed{\dfrac12\cosh(w)\mathrm{Si}(x-iw)+\dfrac12i\sinh(w)\mathrm{Ci}(x-iw)-\dfrac12\cosh(w)\mathrm{Si}(x+iw)+\dfrac12i\sinh(w)\mathrm{Ci}(x+iw)+C}}\end{align} ...

\int_{-\pi/2}^{\pi/2} dx \, \sin^{2n} x

https://math.stackexchange.com/questions/1081610/int-pi-2-pi-2-dx-sin2n-x

Since \int_{-\pi/2}^{\pi/2} e^{2ni\theta}\,d\theta = 0 for any n\in\mathbb{Z}\setminus\{0\}, we have, by expanding (e^{ix}-e^{-ix})^{2n} with the binomial theorem, I=\int_{-\pi/2}^{\pi/2}\left(\frac{e^{ix}-e^{-ix}}{2i}\right)^{2n}\,dx = \frac{(-1)^n}{4^n}\binom{2n}{n}(-1)^n\frac{\pi}{2}=\frac{\pi}{2\cdot 4^n}\binom{2n}{n}. ...

\displaystyle\int\frac{{1}}{{{1}-{{\sin}^{{4}}{\left({x}\right)}}}}{\left.{d}{x}\right.}= ?

https://socratic.org/questions/int-1-1-sin-4x

\displaystyle\frac{{1}}{{2}}{\tan{{x}}}-\frac{{1}}{{{2}\sqrt{{2}}}}\cdot{a}{r}{c}{\tan{{\left(\frac{{1}}{\sqrt{{2}}}\cdot{\cot{{x}}}\right)}}}+{C} . Explanation: Let, \displaystyle{I}=\int\frac{{1}}{{{1}-{{\sin}^{{4}}{x}}}}{\left.{d}{x}\right.} ...

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Exemples

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{ x } ^ { 2 } - 4 x - 5 = 0

Trigonometria

4 \sin \theta \cos \theta = 2 \sin \theta

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]

Equació simultània

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

Diferenciació

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

Integració

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

Límits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

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