Question

complete the following integral or partial substitution with

a. ∫(x^5+2x)/(x^6+6x^2+56)^2 dx

Answer 1

∫(x^5+2x)/(x^6+6x^2+56)^2 dx
∫(x^5+2x) dx - ∫(x^6+6x^2+56)^-2 dx

Answer 2

You can't do this in products, only in additions. suzi20

Answer 3

u = x^6 +6x^2 +56
du = 6x^5 +12x dx
du = 6(x^5 +2x) dx

Answer 4

dv = (x^6+6x^2+56)^-2 dx
v = -1 (x^6+6x^2+56)^-1
uv - ∫ v du
(x^6 +6x^2 +56)(-(x^6+6x^2+56)^-1) - 1/6∫(-(x^6+6x^2+56)^-1) (x^5 +2x) dx
hmm... hard

Answer 5

Suzi please continue the answer

Answer 6

u have to do partial again

Answer 7

Let x^6 + 6x^2 + 56 = t

Now, du = 6x^5 + 12x dx
= 6(x^5 + 2x) dx

The integral becomes,
\[1/6\int\limits_{}{}dt/t^2\]
\[-1/6t\]

Putting back the value of t

= -1/6(x^6+6x^2+56)

Answer 8

I could ask you to complete

Answer 9

that's calculus 2, i remember now, wow amogh cool...........

Answer 10

amogh can I ask you to write down the answer from the first until the end
if you're willing I will be very thankful to you

Answer 11

he did

Answer 12

Tell me what you didn't understand, I've written it completely!

Answer 13

oh I'm sorry, I really do not understand about the calculus lesson, but I want to learn

Answer 14

Let x^6 + 6x^2 + 56 = t

Differentiating on both sides,

Now, dt = (6x^5 + 12x)dx
= 6(x^5 + 2x) dx

Multiplying the integral by 6 and diving by 6,
\[1/6\int\limits_{}^{}6(x^5+2x)/(x^6+6x^2+56)^2 dx\]

Now 6(x^5+2x) becomes dt.

The integral becomes,
\[1/6\int\limits_{}^{} dt/t^2\]
= −1/6t

Putting back the value of t

= -1/6(x^6+6x^2+56)

Answer 15

amogh thanks a lot