i need some help with solving 3 integrals in terms of u. i will post them in a min

Question

anonymous · Answer

$$\int\limits_{2}^{3}6x^2(x^3+1)^4 dx$$
$$\int\limits_{\pi/12}^{\pi/2}x \cos(4x^2)dx$$
$$\int\limits_{2}^{\sqrt{11}}x \sqrt{x^2+5} dx$$

tkhunny · Answer

Have you considered substituting u = "Whatever is inside the parentheses"?

anonymous · Answer

yes that is what i did but from there i dont know how to get it fully in terms of u

tkhunny · Answer

Demonstrate one.

$u = x^{3} + 1$

$du = 3x^{2}\;dx$

Go!

anonymous · Answer

for the first one i would pull the 6 outside and multiply the inside by 3 and the outside by 1/3

tkhunny · Answer

??  Why add a factor of 3 when you already have one sitting there?

$u = x^3 + 1$  This is monotonic, increasing, so there is no confusion.

$2^{3} + 1 = 8 + 1 = 9$

$3^{3} + 1 = 27 + 1 = 28$

Integrand: $6x^{2}\left(x^{3}+1\right)\;dx = 2\left(x^{3}+1\right)\cdot 3x^{2}\;dx = 2u\;du$

$\int_{9}^{28}2u\;du$

anonymous · Answer

oh ok now i understand what i did wrong

tkhunny · Answer

Let's see the next one.