# Tagged Questions

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### Integrating an equation with both cos and tan

$$\int2\cos^5x\cdot\tan^6x\cdot dx$$ $$2\int\cos^5x\cdot\frac{\sin^6x}{\cos^6x}\cdot dx$$ $$2\int \frac{\sin^6x}{\cos{x}} dx$$ $$2\int\cos^{-2}x\cdot \sin^6x\cdot \cos{x}\cdot dx$$ ...
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### Is there a way to integrate $\cos^{2} {3x}$ with a different technique than integration by parts?

The question is just as it is on the title: Is there a way to integrate $\cos^{2} {3x}$ with a different technique than integration by parts? And in case there is, how can I do it?
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### check my solution to indefinite integral problem with arccos

So we had homework it asked us to find $$\int\arccos(x)dx$$ I have found that $$\int\arccos(x)dx=x\arccos (x)+\sqrt{1-x^2}+c$$ Is this right?
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### Trigonometric Substitution

Question: Use the substitution x=3sin(t) to evaluate the integral of I started by making a right triangle and solving for sin(t) and cos(t). sin(t)=x/3 and cos(t)=(sqrt(9-x^2))/3 Then, I solved ...
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### Sine substitution?

My book says the following: $$\int \frac{dx}{(16-x^2)^{3/2}}$$ $$x = 4\sin\theta$$ $$(16 - x^2)^{3/2} = (4^2\cos^2\theta)^{3/2}$$ $$=(4\cos\theta)^3$$ I don't understand the last step: Doesn't: ...
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### Calculus 2 Trigonometric Integrals with odd exponents

I do not know how to go about taking the integral of this. I have tried to break it up so I can take the integral of sin^2(x) sin(x) cos^8(x) cos(x). But then this would require me use the reduction ...
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### Calculus 2 Trigonometric Integrals

I have used the reduction formula for the integral of cos^n(x)dx but was unable to produce a correct answer. I think what throws me off is the (9x). Any helpful hints, tips, or other methods for ...
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### Prove the integral of $\cot x$ is $-\ln|\csc x|+C$

I know how to prove it to be $\ln|\sin x|+C$, but I do not know the method to prove it this way. thanks
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### Looking for the recurrence relation for certain trigonometric integrals

By assuming that: $$\int_{\pi/4}^{\pi/2} \frac{\cos^4(x)}{\sin^5(x)}\,dx = k,$$ what does the integral $$\int_{\pi/4}^{\pi/2} \frac{\cos^6(x)}{\sin^7(x)}\,dx$$ equal in terms of k? I have ...
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### Integral of Form $(a^2 - x^2)^{1/2}$

Solve $\displaystyle \int \dfrac{1}{x^2(9-x^2)^{1/2}}\ \mathrm{d}x$ So far, I have used trigonometric substitution, so that $x = 3\sin y$, $x^2 = 9\sin^2 y$, and $\mathrm{d}x = 3\cos y\ \mathrm{d}y$. ...
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### Integral of cos(5x)cos(3x)cos(4x)dx

The integral $\int_0^{\pi/8}\cos(5x)\cos(3x)\cos(4x) \,dx$ is equal to $k/24$. Find the constant $k$. So far, I assume that the best way to solve this question is to solve the integral and compare ...
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### Integration of exponential trig functions

If $\cos^2x=[1+\cos(2x)]/2=(1/2)[1+\cos(2x)]$ Would I be wrong in assuming that $$\cos^2(3x+1)=\frac{1}{2}\left[1+\cos[2(3x+1)]\right]=\frac{1}{2}\cos(6x+2)+\frac{1}{2}?$$ I'm trying to take the ...
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### Integral of $\int^\sqrt2_1\frac{1}{1+\sqrt{x^2 - 1}}dx$ by substitution?

In a maths question I have the question: $$\int^\sqrt2_1\frac{1}{1+\sqrt{x^2 - 1}}dx$$ by substitution? All other questions have been by trigonometric substitution so I assume that is how to solve. ...
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### Did I solve this integral correctly? (trig substitution)

I'm having trouble with trig substitution. This is what I've done so far, but I'm not sure if I did everything right. This is the integral: $$\int \frac{x^2}{(1+x^2)^\frac{3}{2}}$$ and my ...
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### Definite integral involving arctan and tan

I was solving a problem posed on Moldavian National Mathematical Olympiad for 12th grade in 2012. The question was the following: Problem. Let $f:\mathbb{R}\rightarrow\mathbb{R}$, such that ...
$$\int_0^{\pi/4} \frac {\sin x + \cos x}{\sin^4x+\cos^2x}dx$$ $$\int e^x\cot x(\csc x-1)dx$$ These two integrals are impossible to find. If anyone knows how to integrate them please help me. I am ...