Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

int8x(1)/(2x+1)dx

$\int 8 x \frac{1}{2 x+1} d x$

View step-by-step help

View step-by-step help

Find indefinite integrals using the substitution and by parts

Full solution

Q.

\int 8 x \frac{1}{2 x+1} d x

Define u-substitution: Let's do a u-substitution where $u = 2x + 1$ , then $du = 2dx$ .
Rewrite in terms of $u$ : Rewrite the integral in terms of $u$ : $\int \frac{8x}{2x+1}\,dx = \int \frac{4}{u} \,du$ (since $8x = 4(2x)$ and $2dx = du$ ).
Integrate $4/u$ : Now, integrate $\frac{4}{u}$ with respect to $u$ : $\int \frac{4}{u} \, du = 4\ln|u| + C$ .
Substitute back for u: Substitute back for u to get the integral in terms of x: $4\ln|2x+1| + C$ .

More problems from Find indefinite integrals using the substitution and by parts

Question

\frac{d^{2}}{d x^{2}}\left[5 \ln \left(x^{5}\right)\right]

Posted 3 months ago

Question

Consider the curve given by the equation

x y^{2}-x^{3} y=8

. It can be shown that

\frac{d y}{d x}=\frac{3 x^{2} y-y^{2}}{2 x y-x^{3}}

\newline

Write the equation of the vertical line that is tangent to the curve.

Posted 3 months ago

Question

Consider the curve given by the equation

2 x^{2}-12 x+y^{3}=107

. It can be shown that

\frac{d y}{d x}=\frac{4(3-x)}{3 y^{2}}

\newline

Find the point on the curve where the line tangent to the curve is horizontal.

\newline

(\square

\square)

Posted 3 months ago

Question

Can this differential equation be solved using separation of variables?

\newline

\frac{d y}{d x}=\frac{3}{x^{2} y-8 y}

\newline

1

\newline

\newline

Posted 3 months ago

Question

\begin{array}{c}y=x^{4} \\ \frac{d y}{d x}=\end{array}

Posted 3 months ago

Question

Solve the equation. Check your solution

\newline

19=2-(z+5)

\newline

The solution set is \(\{\longrightarrow\}. (Simplify your answer

Posted 2 months ago

Question

\int \frac{t^{2}}{\sin(1-t^{3})\tan(1-t^{3})} \, dt

Posted 2 months ago

Question

Write the answer in proper scientific notation:

\newline

(8 \times 10^{5} \times 10^{-7})^{4}

Posted 2 months ago

Question

x

and graph the solution on the number line below.

\newline

\frac{x}{-2} < 0

\newline

1

2

\newline

<

\newline

\geq

\newline

\geq

\newline

Inequality Notation:

\newline

Posted 2 months ago

Question

-\int \frac{t^{4}}{(1-t^{2})^{2}} \, dt

Posted 2 months ago