Recent content by b0rsuk

Homework Statement \int x e^-3x dx Homework Equations \int f(x)g'(x) = f(x)g(x) - \int f'(x) g(x) Integration by substitution not allowed The Attempt at a Solution f(x) = x, f'(x) = 1, g'(x) = e^{-3x}, g(x) = \int e^{-3x} dx = -\frac{1}{3}e^{-3x} \int x e^{-3x} dx =...

Oh, I gave up too soon. It's not too hard if you start with the assumption that (x + 4) is a factor in numerator. Case closed :-)

Homework Statement Hello. I have a problem with a innocent-looking integral: \int\frac{x^2 + 7x + 12}{x + 4} dx It doesn't look like i can use the law of sines, because the numerator is of higher order than the denominator. It doesn't look like the numerator is a multiple of the...

Hmm. In such case, 2 \int \sin \frac{x}{2} \cos \frac{x}{2} dx = \int 2 \sin \frac{x}{2} \cos \frac{x}{2} dx = \int \sin x dx = -\cos x + C_1 But what about the first integral ? I know: \sin^2 x + \cos^2 x = 1 But I have: \int\sin^2 \frac{x}{2} + \cos^2\frac{x}{2} dx Can I simply get around...

Homework Statement I'm unable to solve this integral. I get a result, but it doesn't match the solution. \int(sin \frac{x}{2} - cos \frac{x}{2})^2 \mathrm{dx} \int(sin \frac{x}{2} - cos \frac{x}{2})^2 \mathrm{dx} The Attempt at a Solution (attachment?) I'd be grateful for highligting my errors.