Questions tagged [indefinite-integrals]
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Question about finding the primitives of a given function, whether or not elementary.
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Integrating $f(x,y)dx$ for unknown $y$
Is there a way to express an integral such as $$\int (2-y)x^{y-2}dx$$ where $y\equiv y(x)$ we don't know what $y$ is. Is there a way to do this type of integral or do we have to know $y(x)$. calculus integration indefinite-integrals- 420
$f(x)=\sum_{r=1}^{2021} \frac{r}{rx^2-1},\;F(x)=\int f(x)\;dx,\; g(x)=\sum_{r=1}^{2022} \tan\bigg(\frac{\pi r x}{2022}\bigg),\; G(x)=\int g(x)dx.$
Let $$f(x)=\sum_{r=1}^{2021} \frac{r}{rx^2-1},\;F(x)=\int f(x)\;dx,\; g(x)=\sum_{r=1}^{2022} \tan\bigg(\frac{\pi r x}{2022}\bigg),\; G(x)=\int g(x)dx.$$ $A_r=\{x \;|\; f(x)=r, r\in \mathbb R,\; x\in (-... calculus integration ordinary-differential-equations definite-integrals indefinite-integrals- 1,996
Indefinite Integral help [closed]
Can someone help me solve the integral in the link below? [1]: calculus indefinite-integrals- 1
Boundedness proof using the condition given for both functions
Suppose $f$ and $g$ are differentiable functions in $(0,\infty)$ and satisfy $f'(x)(f^5(x) + g^2(x)f(x)) + g'(x) (f^2(x)g(x) + g^3(x))= 0$ show that both f and g are bounded functions my progress : i ... calculus integration derivatives indefinite-integrals- 409
integrating multiplication of complex functions
In my calculations on a problem of quantum optics, I faced an integral of the following form \begin{align} \frac{1}{\pi}\int e^{(\beta^* \alpha)} f(\alpha^*) d^2 \alpha \end{align} with $\alpha$ and ... integration indefinite-integrals complex-integration quantum-mechanics quantum-information- 11
Integrate $\int x\sqrt{1+\sec^4x}dx$
I've been solving some homework in Area of a Surface of Revolution and this integration popped up, I couldn't solve it and can't find anything online about it, plus integral calculator can't solve it ... calculus integration indefinite-integrals solid-of-revolution- 11
Integrating $\frac{1}{x}$
There is a general (mis)conception that $$\int \frac{1}{x} \, \mathrm{d}x = \ln|x| + C \label{1} \tag{1}$$ However, taking the indefinite integral as the set of all functions whose derivative is $\... calculus integration indefinite-integrals- 408
Can integration in which a variable is linked to (itself + constant) be solved?: $\frac{df(x)}{dx}=f(x+5)$ [duplicate]
$$\frac{df(x)}{dx}=f(x+5)$$ I am unable to solve this kind of integration using high school mathematics. Please help. calculus integration indefinite-integrals delay-differential-equations- 21
Solution set of a simple differential equation.
Let $f : \mathbb{R}\to\mathbb{R}$ be differentiable $\forall x \in \mathbb{R}$ Let $f'(x) = f(x) \;\forall x \in \mathbb{R}$ We are asked to find all the functions that satisfy the given constraints. ... calculus ordinary-differential-equations derivatives indefinite-integrals- 29
Using Integration By Parts for $\int\sec^2(x)\tan(x)\,\mathrm dx$ [closed]
Evaluate $\int\sec^2(x)\tan(x)\,\mathrm dx$ I know we can use $\text{substitution}$, but I instinctively used Integration By Parts and am not getting the right answer. What am I missing? integration indefinite-integrals substitution- 19
Evaluation of power times gaussian multivariable integral
In the context of evaluating the propagation of a flattened Gaussian beam, the following integral appears: \begin{equation} \int (\mathbf x^T \mathbf F \mathbf x)^n \exp \left [ - \mathbf x^T \mathbf ... integration multivariable-calculus definite-integrals indefinite-integrals gaussian-integral- 63
Helping in finding an integral
What is the value of the following integral ?! $\int\sqrt{(1+(\frac{x}{h})^{2})^{-1}-b}~~~dx$ I have tried on it as : Let $y=1+(\frac{x}{h})^{2}$ $dy=\frac{2x}{h^{2}}dx$ Thus $dx=\frac{h^{2}}{2x}dy$... calculus integration derivatives definite-integrals indefinite-integrals- 41
$\int \frac{5x^3+2}{\sqrt{x^3+1}}dx$
How do I integrate $\int \frac{5x^3+2}{\sqrt{x^3+1}}dx$ ? I know that the result is $2x\sqrt{x^3+1}$, but I cannot think of a way to get to it. calculus integration indefinite-integrals- 51
Integral of a trigonometric function with an argument of linear function
I would like to know how to do the following integral: $$\int\dfrac{\sin^2(y)}{\sin(x-y)}dy,$$ for $x\in\mathbb{R}$. Wolfram Mathemtica solves it as follows: $$\cos(s + x) + \sin^2(s) \left( \log\left(... real-analysis integration indefinite-integrals trigonometric-integrals- 11
Evaluate the following indefinite integral:
THE QUESTION: $\int \frac {x+3}{\sqrt{5-4x-2x^2}} $ MY WORK: We know the numerator can be expressed in the form of : $ x+3 = A \frac {d}{dx}(5-4x-2x^2) + B$ So we get , $ x+3 = A(-4-4x) +B $ Equating ... integration indefinite-integrals- 35
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