Detailed Explanations for Calculus 2 Equations

Evaluate the indefinite integral.
$\int \frac{3}{x} + \frac{2}{5 x^{6}} d x$

David Young 2021-12-27

Evaluate the definite integral.
$\int_{1}^{4} (8 x^{3} - x) d x$

aramutselv 2021-12-27

Evaluate the indefinite integral.
$\int \frac{2 x^{2} + x}{{(4 x^{3} + 3 x^{2})}^{2}} d x$

Linda Seales 2021-12-27

Find the indefinite integral.
$\int (2 x + 1) e^{x^{2} + x} d x$

eozoischgc 2021-12-27

Evaluate the following integrals.
$\int x 10^{x} d x$

jamessinatraaa 2021-12-27

Find the indefinite integral.
$\int \frac{e^{- x}}{1 + e^{- x}} d x$

Daniell Phillips 2021-12-26

Using Taylor expansion check if series :
$\sum_{n = 1}^{\infty} \sqrt{n} (\arctan (n + 1) - \arctan n)$
converges.

Irvin Dukes 2021-12-26

Use the comparison or limit comparison test to decide if the following series converge.
$\sum_{n = 1}^{\infty} \frac{4 - \sin n}{n^{2} + 1}$
For each series which converges, give an approximation of its sum, together with an error estimate, as follows. First calculate the sum $s_{5}$ of the first 5 terms, then estimate the "tail" $\sum_{n = 6}^{\infty} a_{n}$ by comparing it with an appropriate improper integral or geometric series.

fanyattehedzg 2021-12-26

Evaluate the integrals.
$\int \frac{{(\tan^{- 1} x)}^{5}}{(1 + x^{2})} d x$

eiraszero11cu 2021-12-26

Evaluate the indefinite integral.
$\int \frac{x + \ln x}{x} d x$

hunterofdeath63 2021-12-26

Evaluate the integral.
$\int \frac{\sec 2 x}{\csc 2 x} d x$

Tiffany Russell 2021-12-26

Evaluate the integral.
$\int \frac{1}{x^{2} + 25} d x$

Kathleen Rausch 2021-12-26

Evaluate the indefinite integral.
$\int \frac{x^{6}}{x^{7} + 2} d x$

aramutselv 2021-12-26

Determine the following indefinite integral.
$\int e^{x + 2} d x$

Teddy Dillard 2021-12-25

I am having difficulty finding if this series converges or diverges:
$\sum_{n = 0}^{\infty} \frac{{(- 2)}^{n + 1}}{n^{n - 1}}$
I am unsure of which test to use. At first, I thought I should use alternating series test, but I am unable to manipulate the numerator to ${(- 1)}^{n + 1}$ . I thought I may be able to use root test, but I have no clue how to manipulate the series to do that.
What series test would I use, and how?

compagnia04 2021-12-25

The series is,
$\sum_{n = 9}^{\infty} \frac{1}{n (n - 1)}$

namenerk 2021-12-25

If the Taylor Series of $\ln (x)$ is known:
$\ln (x) = (x - 1) - \frac{1}{2} {(x - 1)}^{2} + \frac{1}{3} {(x - 1)}^{2} - \frac{1}{4} {(x - 1)}^{4} + \frac{1}{5} {(x - 1)}^{5} - \dots$
Can one find the Taylor series of
$f (x) = \frac{x}{1 - x^{2}}$
by manipulating the Taylor series of $\ln (x)$ ?

untchick04tm 2021-12-23

Find the Maclaurin series for $f (x) = \frac{x^{2}}{1 - 8 x^{8}}$

Brock Brown 2021-12-23

The series $2 [\frac{1}{3 x + 1} + \frac{1}{3 {(3 x + 1)}^{3}} + \frac{1}{5 {(3 x + 1)}^{5}} + \dots]$ is equal to?

Nicontio1 2021-12-23

I was asked to compute this series:
$\sum_{n = 1}^{\infty} \frac{1}{{(2 n - 1)}^{2}}$
but by using the fact that $\sum_{n = 1}^{\infty} \frac{1}{n^{2}} = \frac{π^{2}}{6}$

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More