$\int \frac{1}{x\sqrt{x}}dx$ | What is integral of 1/x√x

You can reach integral of 1/x√x answer on this page.

What is integral of ∫1/x√x.dx?

integral of 1/x√x

Question:

$\int \frac{1}{x\sqrt{x}}dx$

Solution:

$\int \frac{1}{x\sqrt{x}}dx=\int x^{-\frac{3}{2}}dx=-\frac{2}{\sqrt{x}}+C$

Answer:

$\int \frac{1}{x\sqrt{x}}dx=-\frac{2}{\sqrt{x}}+C$

Read More

$\int sin^5{x}dx=?$ | What is integral of sinx^5

You can reach integral of sinx^5 answer on this page.

What is integral of ∫sinx^5dx?

integrate of sinx^5

Evaluate $\int sin^5{x}dx$.

Rewrite the function:

$\int sin^5{x}.dx=\int sinx.sin^4x.dx=\int sinx(sin^2x)^2.dx=\int sinx(1-cos^2x)^2.dx$

Now use u=cosx, du=-sinxdx:

$\int sinx(1-cos^2x)^2.dx=\int -(1-u^2)^2du=\int -(1-2u^2+u^4)du$

=$-u+\frac{2}{3}u^3-\frac{1}{5}u^5+C$

=$-cosx+\frac{2}{3}cos^3x-\frac{1}{5}cos^5x+C$

Answer: 

$\int sin^5{x}.dx=-cosx+\frac{2}{3}cos^3x-\frac{1}{5}cos^5x+C$

Read More

$\int \frac{lnx^2}{x}.dx=?$ | What is integral of lnx^2/x?

You can reach integral of (lnx^2)/x answer on this page.

What is integral of ∫lnx^2/xdx?

Question:

$\int \frac{lnx^2}{x}.dx=?$

lnx^2/x integrate

Solution:

Substituting u = lnx and $du = \frac{1}{x}dx$ , you get

$\int \frac{lnx^2}{x}dx=\int \frac{2lnx}{x}dx=2.\int u.du=2.\frac{1}{2}u^2+C = (lnx)^2+C$

$\int \frac{lnx^2}{x}.dx=(lnx)^2+C$

Read More

$x.e^{x^2}$ integral | What is integral of x.e^(x^2) ?

You can reach integral of $x.e^{x^2}$ solutions.

What is integral of $x.e^{x^2}$ ?

x.e^x2 integrate solution

Solution:

$\int x.e^{x^2}dx=?$

Substituting $u = x^2$ and $\frac{1}{2} du = x.dx$, you get

$\int x.e^{x^2}dx=\frac{1}{2}\int e^u = \frac{1}{2}e^u+C=\frac{1}{2}e^{x^2}+C$

Read More

Graph of sin | What is the sin(x) graph drawing?

Hello everyone dear friends. In this lesson, we will share with you what the sin graph is.

What is the graph of sin(x)?

The plot of sin(x) is as follows:

sin graph

sinx graph

sinx graph

Here are 3 different sinx charts.

All three graphs are sinx's graphs. You can use all three. Thank you so much. We wish you success in your work.

Read More

Graph of cos | What is the cos(x) graph drawing?

Hello everyone dear friends. In this lesson, we will share with you what the cos graph is.

What is the graph of cos?

The plot of cos(x) is as follows:

cos graph

graph of cosx

Both graphs are graphs of cos. You can use both. Thank you so much. We wish you success in your studies.

Read More

How to find the slope of a graph? (Examples and answers)

Hello everyone, in this article, we will tell you how to find the slope of a graph and how to calculate it with examples. We wish you a good work ahead...

How to find the slope of a graph?

The slope of a line is determined by the ratio $\frac{change in y}{change in x}$ between any two points that lie on the line.

The slope is the constant rate of change of a line.

Example:

Use a graph to determine the slope of a line.

Slope of graph = -1/2

Step 1: Identify two points on the line. In this case, use (0, 2) and (2, 1).

Step 2: Calculate the vertical change from one point to the next. In this case, you must count down 1 space to move from the point (0, 2) to the point (2, 1).

Step 3: Calculate the horizontal change from one point to the next. In this case, you must count right 2 spaces to move from the point (0, 2) to the point (2, 1).

Step 4: Write the ratio showing $\frac{vertical change}{horizontal change}$ in simplest form.

In this case, the slope is represented by the ratio $\frac{-1}{2}$ , or $-\frac{1}{2}$ .

Solution: The slope is negative because the line falls from left to right.

Answer = -1/2

Practice:

Source : collegeboard.org

Read More