Evaluate the integrals in Exercises 31–78.
33. ∫e^x sec²(e^x - 7)dx

Evaluate the integrals in Exercises 33–54.

∫ 2t e^(-t²) dt

Evaluate the integrals in Exercises 33–54.

∫ (e^(1/x) / x²) dx

Evaluate the integrals in Exercises 33–54.

49. ∫ e^(sec πt) sec πt tan πt dt

Evaluate the integrals in Exercises 31–78.

31. ∫e^x sin(e^x)dx

Evaluate the indefinite integral. 

${\int }_{}^{}-{\left(6\right)}^{x}dx$

Evaluate the indefinite integral.

${\int }_{}^{}3x^4-{\left(5\right)}^{x}dx$

Evaluate the indefinite integral.

${\int }_{}^{}2{\left(\frac{1}{3}\right)}^{x}dx$

Evaluate the definite integral.

${\int }_0^5\frac{3^{\sqrt{x+4}}}{\sqrt{x+4}}dx$