# Tagged Questions

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### Is the following integration of possible?

How to solve the following problem? $\int x^4/(1-x^4)^{3⁄2}dx$ I have tried the substitution, x=sinz, but failed.
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### Antiderivative of $\frac{1}{1+\sin {x} +\cos {x}}$

How do we arrive at the following integral $$\displaystyle\int\dfrac{dx}{1+\sin {x}+\cos {x}}=\log {\left(\sin {\frac{x}{2}}+\cos {\frac{x}{2}}\right)}-\log {\left(\cos {\frac{x}{2}}\right)}+C\ ?$$
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### Determine the indefinite integral $\int \frac{\sin x}{\sin 5x}dx$ [closed]

Find the value of the given integral $$\int \frac{\sin x}{\sin 5x}dx$$
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### How to evaluate the following integral? $\int \frac{x^6}{x^4-1} \, \mathrm{d}x.$

Evaluate the integral: $$\int \frac{x^6}{x^4-1} \, \mathrm{d}x$$ After a lot of help I have reached this point: $x^2 = Ax^3 - Ax + Bx^2 - B + Cx^3 + Cx^2 + Cx + C + Dx^3 - Dx^2 + Dx - D$ But now I ...
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### How to calculate $\int\frac{1}{x + 1 + \sqrt{x^2 + 4x + 5}}\ dx$?

How to calculate $$\int\frac{1}{x + 1 + \sqrt{x^2 + 4x + 5}}dx?$$ I really don't know how to attack this integral. I tried $u=x^2 + 4x + 5$ but failed miserably. Help please.
Integrate , for $\alpha > 2$ $\int_0^{\infty}\!\frac{x-1}{x^\alpha-1}\, dx.$ I would be intertest for any replies or any comments