$\int \frac{1}{x.lnx}.dx=?$ | What is integral of 1/x.lnx?

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

What is integral of ∫1/x.lnx.dx?

Question:

$\int \frac{1}{x.lnx}.dx=?$

Solution:

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

$\int \frac{1}{x.lnx}.dx=\int \frac{1}{u}.du=ln|u|+C = ln|lnx| + C$

$\int \frac{1}{x.lnx}.dx=ln|lnx| + C$

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Homework: In problems 1 through 20 find the area of the region R

Questions and answers of find area of region problems.

1-) R is the triangle bounded by the line y = 4 − 3x and the coordinate axes.

Answer = $\frac{8}{3}$

2-) R is the rectangle with vertices (1, 0), (−2, 0), (−2, 5) and (1, 5).

Answer = 15

3-) R is the trapezoid bounded by the lines y = x + 6 and x = 2 and the coordinate axes.

Answer = 14

4-) R is the region bounded by the curve $y = \sqrt{x}$ , the line x = 4, and the x axis.

Answer = $\frac{16}{3}$

5-) R is the region bounded by the curve $y = 4x^3$ , the line x = 2, and the x axis.

Answer = 16

6-) R is the region bounded by the curve $y = 1 − x^2$ and the x axis.

Answer = $\frac{4}{3}$

7-) R is the region bounded by the curve $y = −x^2 − 6x − 5$ and the x axis

Answer = $\frac{32}{3}$

8-) R is the region in the first quadrant bounded by the curve $y = 4 − x^2$ and the lines y = 3x and y = 0.

Answer = $\frac{19}{6}$

9-) R is the region bounded by the curve $y = \sqrt{x}$ and the lines y = 2 − x and y = 0.

Answer = $\frac{7}{6}$

10-) R is the region in the first quadrant that lies under the curve $y = \frac{16}{x}$ and that is bounded by this curve and the lines y = x, y = 0, and x = 8.

Answer = 8(1+ln4)

11-) R is the region bounded by the curve $y = x^2−2x$ and the x axis. (Hint: Reflect the region across the x axis and integrate the corresponding function.)

Answer = $\frac{4}{3}$

12-) R is the region bounded by the curves $y = x^2 + 3$ and $y = 1 − x^2$ between x = −2 and x = 1.

Answer = 12

13-) R is the region bounded by the curve $y = e^x$ and the lines y = 1 and x = 1.

Answer = e-2

14-) R is the region bounded by the curve $y = x^2$ and the line y = x.

Answer = $\frac{1}{6}$

15-) R is the region bounded by the curve $y = x^2$ and the line y = 4.

Answer = $\frac{32}{3}$

16-) R is the region bounded by the curves $y = x^3 − 6x^2$ and $y = −x^2$.

Answer = $\frac{625}{12}$

17-) R is the region bounded by the line y = x and the curve $y = x^3$.

Answer = $\frac{1}{2}$

18-) R is the region in the first quadrant bounded by the curve $y = x^2 + 2$ and the lines y = 11 − 8x and y = 11.

Answer = $\frac{40}{3}$

19-) R is the region bounded by the curves $y = x^2 − 3x + 1$ and $y = −x^2 + 2x + 2$.

Answer = $\frac{11}{8}\sqrt{33}$

20-) R is the region bounded by the curves $y = x^3 − x$ and $y = −x^2 + x$.

Answer = $\frac{37}{12}$

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What is integral of x^3/4 | $\int x^{\frac{3}{4}}.dx=?$

You can reach integral of x^3/4 answer on this page.

What is integral of ∫x^3/4.dx?

integral of x^3/4

$\int x^{\frac{3}{4}}.dx=\frac{4}{7}.x^{\frac{7}{4}}+C$

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$x.e^{-x}$ integral | What is integral of x.e^-x? | $\int x.e^{-x}.dx=?$

You can reach integral of x.e^-x answer on this page.

What is integral of ∫x.e^-x.dx?

x.e^-x integral

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

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

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

What is integral of ∫x.lnx^2.dx?

Solution. In this case, the factor $X$ is easy to integrate, while the factor ln $x^2$ is simplified by differentiation. This suggests that you try integration by parts with:

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

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What is integral of 1/x^2? What is the integral of one over x squared?

You can reach integral of 1/x^2 or x^-2 (one over x square) answer on this page.

What is integral of 1/x^2?

1/x^2 integral

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

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Integral of 3x^2-√5x+2 | What is integral of ∫(3x^2-√5x+2).dx?

You can reach integral of 3x^2-√5x+2 answer on this page.

What is integral of  ∫(3x^2-√5x+2).dx?

integral of 3x^2-root 5x+2

$\int (3x^2-\sqrt{5x}+2).dx=x^3-\frac{2}{3}.x.\sqrt{5x}+2x$

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