11. Integrals of Inverse, Exponential, & Logarithmic Functions

What is the indefinite integral of $e^{5x}$ with respect to $x$?

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.

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

Find the area under the graph of $f\left(x\right)=3^{2x}$ between $x=0$ and $x=2$.

Evaluate the indefinite integral.

${\int }_{}^{}(\sqrt{x}-e^x)dx$

Evaluate the indefinite integral.

${\int }_{}^{}(4e^x+\frac{1}{x^3})dx$

Evaluate the indefinite integral.

${\int }_{}^{}\frac{e^{2\sqrt{x}}}{\sqrt{x}}dx$

Evaluate the indefinite integral.

${\int }_{}^{}{e}^{\sec \theta }\sec \theta \tan \theta d\theta$

Find the definite integral.

${\int }_{-1}^1{x}^2{e}^{x^3}dx$

Find the area of $f\left(x\right)=3+e^{2x}$ from $x=0$ to $x=2$.

7–84. Evaluate the following integrals.

33. ∫ [eˣ / (a² + e²ˣ)] dx, where a ≠ 0

Evaluate the following integrals.

∫ e³ˣ/(eˣ - 1) dx

7–40. Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.

40. ∫ (e³ᵗ / √(4 + e²ᵗ)) dt