Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Continue

Input your name and email to request the answer

Like

Report

Determine $G^{\prime}(x)$ if $G(x)=\int_{e^{2x}}^{x^{3}} \frac{x}{x^{2}+1} d x$.

$$\frac{3 x^{5}}{x^{6}+1}-\frac{2 e^{4 x}}{e^{4 x}+1}$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 7

Substitution and Properties of Definite Integrals

Integrals

Campbell University

Baylor University

University of Nottingham

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

02:21

Calculate.$$\int \frac…

02:12

Find $\int x^{3} e^{x^{2}}…

0:00

How to solve this question…

00:35

$$\begin{array}{l}{\te…

01:06

Find $\int_{-1}^{2}[f(x)+2…

02:46

Calculate.$$\int x^{3}…

02:23

Calculate.$$\int x^{2}…

01:56

Determine $\int \frac{x^{2…

01:53

03:57

FInd the integral

No transcript available

View More Answers From This Book

Find Another Textbook

02:59

Consider the parabola $f(x)=a x^{2},$ with $a>0 .$ When $x=b,$ call the $…

01:52

Determine the area of the indicated region.Region bounded by $f(x)=2 / x…

01:38

$u(x, y)$ is said to be harmonic if it is a solution to the partial differen…

00:57

Determine the region $R$ determined by the given double integral.$$\int_…

01:43

Determine $G(x)$.$$G(x)=\int_{0}^{x} t^{2} d t$$

02:01

Evaluate the double integral $\int_{R} \int f(x, y) d A$ over the indicated …

03:22

The partial differential equation $c^{2} u_{x x}-u_{t t}=0$ where $c$ is a c…

03:45

Determine the area of the indicated region.Region bounded between $f(x)=…

03:10

Evaluate $\int_{R} \int f(x, y) d A$ for $R$ and $f$ as given.(a) $f(x, …

01:09