# Tagged Questions

Question about finding the primitives of a given function, whether or not elementary.

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### Integration of $\int \frac{1}{x^{1/3}(x^{1/3}-1)}dx$ [closed]

Integrate the following function $$\int \frac{1}{x^{1/3}(x^{1/3}-1)}dx$$ Could someone give me slight hint to solve this question?
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### Can you solve this integral [closed]

I tried to solve this integral, but I couldn't; I don't know by what substitution or by what method. Can you help me to find its exact solution? $$\int\frac {1}{3^x+x}dx$$
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### Need help solving $\int\frac{\sin(x+1)\cos(x)}{\sin^2(x)+4} dx$

As the title says I need help solving the indefinite integral $$\int\frac{\sin(x+1)\cos(x)}{\sin^2(x)+4}dx$$ Thank you for any help.
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### Integrating by substitution containing a further factor problem

The problem: $${\int } (x+1)(3x+1)^9 dx$$ let u = 3 x +1 3 x = u - 1 $x = \frac{1}{3} (u-1)$ Hence, $x + 1 = \frac{1}{3} (u-1) + 1$ $= \frac{1}{3} (u+2)$ This line here I do not ...
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I'm stuck at this problem: $$\int{\sqrt{(\sin^2 x)^2 + (2\sin x \cos x)^2}dx} = \int{\sqrt{\sin^2 x \sin^2 x + 4\sin^2 x \cos^2 x} dx}$$ I tried a few trig identities: $\sin^2 x = \frac{1-\cos 2x}{... 2answers 80 views ### Solve integral$\int \frac{x+1}{x^2-2x+5} dx$I need to solve: $$\int \frac{x+1}{x^2-2x+5} dx$$ I cann see that$D>N$so I tried to scompose the$D$but I get: $$x_{1,2} = \frac{2 \pm \sqrt{4-20}}{2}$$ So$\Delta < 0$and I tried to use ... 1answer 17 views ###$\int(\int\phi(a-z)dz)dz=\Phi(a-z)$Lets assume$\phi(a-z)$is integrable. Can I conclude that the following integral $$\int\left(\int\phi(a-z)dz\right)dz$$ Can be expressed by a function $$\Phi(a-z).$$ So in result: $$\int\left(\... 1answer 49 views ### Find antiderivative of ln(x)^y for any real y What is this antiderivative? I have tested several values of y in an online antiderivative calculator, but it's not clear how they are related. Here y is fixed and I want the antiderivative with ... 2answers 72 views ### Solve the differential equation:\frac{\,dx}{mz-ny}=\frac{\,dy}{nx-lz}=\frac{\,dz}{ly-mx} QUESTION: Solve the differential equation:$$\frac{\,dx}{mz-ny}=\frac{\,dy}{nx-lz}=\frac{\,dz}{ly-mx}$$MY ATTEMPT: I tried out to proceed by using$$\frac{\,dx}{mz-ny}=\frac{\,dy}{nx-lz}=\frac{\,... 3answers 112 views ### Solution of integral$\int \frac{\sin (x)}{\sin (5x) \sin (3x)} dx$Find the following integral $$\int \frac{\sin (x)}{\sin (5x) \sin (3x)} dx$$ I don't know how to deal with the$\sin (x)$in the numerator. If it had been$\sin (2x)$then we could have used$\sin (...
$\newcommand{\dx}{\,\mathrm dx}$ I need to find the following: $$\int \sqrt{\frac{1-x}{1+x}} \cdot \frac 1x \dx$$ Firstly, it has to be that $x\in (-1, 0)\cup (0,1]$. From this, it is implied ...