How do you do this question?

Step-by-step explanation:

∫₁² [e^(1/x⁴) / x⁵] dx

∫₁² [e^(x⁻⁴) x⁻⁵] dx

If u = x⁻⁴, then du = -4x⁻⁵ dx, and -¼ du = x⁻⁵ dx.

∫ e^u (-¼ du)

-¼ ∫ e^u du

-¼ e^u + C

-¼ e^(x⁻⁴) + C

Evaluate between x=1 and x=2.

-¼ e^(2⁻⁴) − -¼ e^(1⁻⁴)

-¼ e^(1/16) + ¼ e

(e − ¹⁶√e) / 4

Step-by-step explanation:

So we have the definite integral:

Again, we can use u-substitution. Let u equal 1/x^4. So:

Find the derivative:

Divide by -4. So du is:

Of course, we also need to change our bounds. Substitute 1 and 2 into u:

Therefore, our new bounds are from 1 to 1/16.

So, make the substitutions:

The integral of e^u is just e^u. So:

Evaluate for the bounds:

Simplify:

Distribute:

And we're done!

where r the answers

step-by-step explanation: