Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.
∫ (ln x)³/x dx

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

73. ∫(from 0 to π)cos(x)dx/√(1+sin²x)

Evaluate the integrals in Exercises 1–6.

∫ dt / (t - √(1 - t²))

Evaluate the integrals in Exercises 53–76.

69. ∫dx/((2x-1)√((2x-1)²-4))

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

71. ∫(from 1/5 to 3/13)dx/(x√(1-16x²))

Find the indefinite integral.

${\int }_{}^{}\frac{3-y^2}{2y}dy$

Evaluate the definite integral.

${\int }_2^e\frac{3+x}{x}dx$

Find the area under the graph of $f\left(t\right)=\frac{t^2{e}^t+t}{t^2}$ from $t=1$ to $t=3$.

Find the indefinite integral.

${\int }_{}^{}\frac{1}{2x+5}dx$