In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.
37. ∫(from x²/2 to x²)ln(√t)dt

Differentiating Integrals

In Exercises 75–78, find dy/dx.

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y = ∫₂ˣ √ 2 + cos³t dt

In Exercises 75–78, find dy/dx.

y = ∫(from x to 1) (6/(3 + t^4))dt

Find dy/dx if y = ∫ₓ¹ √(1 + t²)dt.

Explain the main steps in your calculation.

Find dy/dx if y = ∫(From cos x to 0) 1/(1 - t²) dt.

Explain the main steps in your calculation.

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = ∫(from 0 to lnx) sin(e^t) dt

Evaluate the integrals in Exercises 111–114.

111. ∫₁^(ln x) (1 / t) dt,x > 1

Evaluate the integrals in Exercises 111–114.

113. ∫₁^(1/x) (1 / t) dt,x > 0

For Exercises 127 and 128 find a function f satisfying each equation.

128. f(x) = e² + ∫₁ˣ f(t) dt