kadetskihykw

2022-05-03

What is $$\int \frac{4}{5(4t+4)}dt$$?

Assainato9gf

Beginner2022-05-04Added 15 answers

Cancel the common factor of 4 and 4t+4.

$$\int \frac{1}{5(t+1)}dt$$

Since $$\frac{1}{5}$$ is constant with respect to t, move $$\frac{1}{5}$$ out of the integral.

$$\frac{1}{5}\int \frac{1}{t+1}dt$$

Let u=t+1. Then du=dt. Rewrite using u and du.

$$\frac{1}{5}\int \frac{1}{u}du$$

The integral of $$\frac{1}{u}$$ with respect to u is $$\mathrm{ln}(|u|)$$

$$\frac{1}{5}(\mathrm{ln}(|u|)+C)$$

Simplify

$$\frac{1}{5}\mathrm{ln}(|u|)+C$$

Replace all occurrences of u with t+1

$$\frac{1}{5}\mathrm{ln}(|t+1|)+C$$

$$\int \frac{1}{5(t+1)}dt$$

Since $$\frac{1}{5}$$ is constant with respect to t, move $$\frac{1}{5}$$ out of the integral.

$$\frac{1}{5}\int \frac{1}{t+1}dt$$

Let u=t+1. Then du=dt. Rewrite using u and du.

$$\frac{1}{5}\int \frac{1}{u}du$$

The integral of $$\frac{1}{u}$$ with respect to u is $$\mathrm{ln}(|u|)$$

$$\frac{1}{5}(\mathrm{ln}(|u|)+C)$$

Simplify

$$\frac{1}{5}\mathrm{ln}(|u|)+C$$

Replace all occurrences of u with t+1

$$\frac{1}{5}\mathrm{ln}(|t+1|)+C$$

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

$f(x,y)={x}^{3}-6xy+8{y}^{3}$ $\frac{1}{\mathrm{sec}(x)}$ in derivative?

What is the derivative of $\mathrm{ln}(x+1)$?

What is the limit of $e}^{-x$ as $x\to \infty$?

What is the derivative of $f\left(x\right)={5}^{\mathrm{ln}x}$?

What is the derivative of $e}^{-2x$?

How to find $lim\frac{{e}^{t}-1}{t}$ as $t\to 0$ using l'Hospital's Rule?

What is the integral of $\sqrt{9-{x}^{2}}$?

What is the derivative of $f\left(x\right)=\mathrm{ln}\left[{x}^{9}{(x+3)}^{6}{({x}^{2}+7)}^{5}\right]$ ?

What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?

How to find the derivative of $y={e}^{5x}$?

How to evaluate the limit $\frac{\mathrm{sin}\left(5x\right)}{x}$ as x approaches 0?

How to find derivatives of parametric functions?

What is the antiderivative of $-5{e}^{x-1}$?

How to evaluate: indefinite integral $\frac{1+x}{1+{x}^{2}}dx$?