Apr 6, 2017 · I had just started learning Calculus recently and I encountered an Integral that was not talked about on my textbook, for example: $$\\int_1^0x\\sqrt{x-1}\\,dx$$ How do I solve this integral step by ...

The idea is to get a square under the square root ... {x^2 + a^2} = -x + t$$ transforms the integral to ...

I need to learn how to find the definite integral of the square root of a polynomial such as: $$\sqrt{36x + 1}$$ or $$\sqrt{2x^2 + 3x + 7} $$ EDIT: It's not guaranteed to be of the same form. It could be any polynomial that can't be easily factored into squares.

Feb 21, 2018 · I was trying to do this integral $$\\int \\sqrt{1+x^2}dx$$ I saw this question and its' use of hyperbolic functions. I did it with binomial differential method since the given integral is in a form o...

Integral of square root of a fraction of two functions. 2. Integral of square of variable in expression in ...

Mar 1, 2017 · For example, how do I calculate the indefinite integral of the square root of x? I understand how the power rule works, but im confused by the square root. I would appreciate any help given!

Dec 21, 2015 · Find $\\displaystyle \\int \\sqrt{\\tan(x)}dx$. According to an integral calculator, the answer to this question is $$(-2 \\tan^{-1}(1-\\sqrt(2) \\sqrt(\\tan(x)))+2 ...

Jul 18, 2017 · When you are solving an integral, and you have a square root of a square, for instance $$ \int \sqrt{1+\cos x} = \int \sqrt{\frac{\sin^2x}{1-\cos x}}$$ Do I have to take the absolute value of $\sin x$, or can I just take the positive value?

Mar 17, 2015 · A different approach, building up from first principles, without using cos or sin to get the identity, $$\arcsin(x) = \int\frac1{\sqrt{1-x^2}}dx$$ where the integrals is from 0 to z.

I have been having extreme difficulties with this integral. I would appreciate any and all help. $$ \\int \\sqrt{\\tan x} ~ \\mathrm{d}{x}. $$