Please Calculus Evaluate the Integral:?

Question

} sin t / (7 + cos t )^5

Answer 1

To solve this, first bring the (7+cost)^5 to the numerator, making the 5 a negative. Then use u substitution.
The u is 7 + cos t, du is -sint. Move the negative to the left of the integral. Now you have
- } u^-5 du
Integrate this to get (u^-4)/-4 + C (unknown constant). Multiply the first term by the negative sign, and your final answer is

[1 / 4(7+ cost)^4] + C

(notice I also substitued the 7 + cos t for the u we had earlier.)

Hope this helps!

Answer 2

I think you have to solve this using substitutions. Let u=7 + cos t which will give du= -sin t dt. Also, bring the denominator up. so it'll be : Integral sin t (7 +cos t)^-5 dt. I believe the answer will be 1/4 (7+cos t)^-4 + C

Answer 3

I = ∫ sin t /(7 + cos t)^(5) dt
Let u = 7 + cos t
du = - sin t dt
- du = sin t dt
I = - ∫ du / u^(5) = - ∫ u^(-5) du
I = 1 / 4u^(4) + C
I = 1 / (4.(7 + cos t)^(4)) + C

Answer 4

put cos t+7 =z
Then dz = -sint dt
Substitution makes it I(dz/z^5)
I() represents integration

So the integrated function is z^-4/-4 = -1/4(cos t + 7)^4