# Tagged Questions

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### Steps to solve $\int \sqrt{\frac{11}{x}}\,\mathrm{d}x$?

What are the steps required to solve the following? $\int \sqrt{\frac{11}{x}}\,\mathrm{d}x$ I'm not looking for anyone to do my homework. I usually have no problem figuring these things out -- ...
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### Evaluate $\int \sqrt{1-x^2}\,dx$

I have a question to calculate the indefinite integral: $$\int \sqrt{1-x^2} dx$$ using trigonometric substitution. Using the substitution $u=\sin x$ and $du =\cos x\,dx$, the integral becomes: ...
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### How do I solve this Integral using an infinite series

I'm supposed to use an infinite series to solve $$\int\frac{e^{2x}}{x}dx$$ How do I solve this? I know the answer already, I don't even have to use infinite series to solve this, however it was ...
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### How to solve $\int \frac{\,dx}{(x^3 + x + 1)^3}$?

How to solve $$\int \frac{\,dx}{(x^3 + x + 1)^3}$$ ? Wolfram Alpha gives me something I am not familiar with. I thought that the idea was using partial fractions because $x^3$ and $x$ are ...
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### How to solve this first order non-linear ODE

I am struggling to solve this first order ODE. $$u'\,^2 = a u^2 + b u^3$$ Mathematica gives me, $$u(v) = \dfrac{a}{b} \mathrm{sech} \left( \dfrac{1}{2} \sqrt{a} \ (v + c) \right)^2$$ So I ...
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### Integration - U substitution

I am given the following indefinite integral: $\int x\sqrt{1+2x}~dx$ using the substitution $u=\sqrt{1+2x}$ I am not sure where to begin, I know that $du=\dfrac{1}{\sqrt{1+2x}}$ But how can I get ...
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### How do I determine the values of $r$ so $e^{t^r}$ has an antiderivative?

It's fairly easy to show for individual values of $r$, just plug in the value and try it, but is there any way to find, in general, which values of $r$ work so that $\int{e^{t^r}dt}$ can be expressed ...
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### How can I solve$\int \sin^3(x)dx$?

I have to find the integral $$\int \sin^3xdx\\= \int \sin^2x \sin xdx\\= \int (1-\cos^2x) \sin xdx$$ Substitution: $$z=\cos x$$ $$\frac{dz}{dx} = -\sin x$$ $$-dz = \sin x dx$$ Now the above ...
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### Evaluating the indefinite integral

I am having trouble understanding this homework question: $$\int \frac {dx}{cx+h}$$ So, what I thought I should do is... $$\int \frac {dx}{cx+h}$$ let $u$ be: $cx+h$ let $du$ be: $1\,dx$ ...
### $\int\sqrt{1-\cos2x}~dx=$ ?
So here is the problem I'm working with $$\int\sqrt{1-\cos2x}~dx$$ I'm assuming that I'll need to use the trig identity $2\sin^2x=1-\cos2x$ . But where do I go from there? ...