$e^{1-x}dx$ integral | What is integral of e^1-x ?

You can reach integrate of e^1-x solution and answer.

What is integral of $e^{1-x}dx$ ?

integrate of e^1-x

Answer:

$\int e^{1-x}dx=?$

$\int e^{1-x}dx=-e^{1-x}+C$

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

Hello everyone dear friends. In this lesson, we will share with you what the tangent(x) graph is.

What is the graph of tanx?

The plot of tan(x) is as follows:

tangent graph

graph of tan(x)

Both graphs are graphs of tangent(x). You can use both. Thank you so much. We wish you success in your studies.

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$\int \frac{x^2+1}{x^2-1}dx=?$ | What is integral of (x^2+1)/(x^2-1)

You can reach integral of (x^2+1)/(x^2-1) answer on this page.

What is integral of $\int \frac{x^2+1}{x^2-1}dx$?

integral of (x^2+1)/(x^2-1)

Solution:

Performing polynomial long division, we have that:

$\int \frac{x^2+1}{x^2-1}dx=\int (1+\frac{2}{x^2-1})dx$

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

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

Using partial fraction on the remaining integral, we get:

$\frac{2}{x^2-1}=\frac{A}{x-1}+\frac{B}{x+1}=\frac{A(x+1)+B(x-1)}{(x+1)(x-1)}=\frac{(A+B)x+(A-B)}{x^2-1}$

Thus, A + B = 0 and A − B = 2. Adding the two equations together yields 2.A = 2, that is, A = 1, and B = − 1. So, we have that:

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

Therefore,

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

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

$=x+ln|x-1|-ln|x+1|+C$

Answer : 

$\int \frac{x^2+1}{x^2-1}dx=x+ln|x-1|-ln|x+1|+C$

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

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

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$\int sin^5{x}dx=?$ | 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: 

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

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

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

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

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$x.e^{x^2}$ 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

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

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