Question

Evaluate the integral. ∫ (sec^2 (t) i + t(t^2 +1)^7 j + t^4 In(t) k)dt

Answer 1

Explanation:

The integral of the given expression ∫ (sec^2(t) i + t(t^2 + 1)^7 j + t^4 ln(t) k) dt is:

∫ sec^2(t) i dt + ∫ t(t^2 + 1)^7 j dt + ∫ t^4 ln(t) k dt

= tan(t) i + (1/16) * (t^2 + 1)^8 j + (1/5) * t^5 ln(t) - (1/25) * t^5 k + C

Here, C represents the constant of integration.

Answer 2

C

Explanation:

sec^2(t) dt = tan(t) + C₁, ∫ t(t^2 + 1)^7 dt = (1/30) * (t^2 + 1)^8 + C₂, ∫ t^4ln(t) dt = (1/5) * t^5 * ln(t) - (1/25) * t^5 + C₃,