Indefinite Integral

[CatchThis2]

(5/x^6)- 4 to the third root of x^2

So far I made u=x^2
du/dx=1
du=dx

Where do I go from here?

 

[Deleted member 4993]

(5/x^6)- 4 to the third root of x^2

So far I made u=x^2
du/dx=1<<< Incorrect du/dx = 2x
du=dx

Where do I go from here?

Is your problem:

\(\displaystyle \int_4^{x^{\frac{2}{3}}}\frac{5}{x^6}dx\)

If not please try to describe it again.

 

[CatchThis2]

No , it is this.

Evaluate the integral: 5 divided by x to the 6, minus 4 to the cubed root of x squared.

 

[Deleted member 4993]

No , it is this.

Evaluate the integral: 5 divided by x to the 6, minus 4 to the cubed root of x squared.

What does - 4 to the - mean? 4 to the power like:

\(\displaystyle 4^{x^{\frac{2}{3}}\)

 

[CatchThis2]

This is what it should look like

 

[Deleted member 4993]

This is what it should look like

That is a horse of a different color. Your problem becomes:

\(\displaystyle 5\cdot \int x^{-6} dx \ - \ 4\cdot \int x^{\frac{2}{3}} dx\)

No substitution necessary. Continue....

 

[CatchThis2]

So now I have 5 x^-7/-7 minus 4 x^2/3

Substitute in so I should have -5/7 x^-7 minus 4^2/3

 

[lookagain]

This is what it should look like

CatchThis2,

use grouping symbols, and then you may interpret it as one of the acceptable forms
that Subhotosh Khan's rewrite showed:

\(\displaystyle \int\bigg(\frac{5}{x^6} \ - \ 4\sqrt[3]{x^2}\bigg)dx =\)

\(\displaystyle 5\cdot \int x^{-6} dx \ - \ 4\cdot \int x^{\frac{2}{3}} dx\)

So now I have 5 x^-7/-7 minus 4 x^2/3

\(\displaystyle . . . You \ \ didn't \ \ find \ \ the \ \ correct \ \ antiderivatives,\)
\(\displaystyle \ \ and \ \ you \ \ left \ \ off \ \ the \ \ "+ C."\)

Substitute in so I should have -5/7 x^-7 minus 4^2/3 . . . \(\displaystyle This \ is \ not \ correct.\)

CatchThis2,

you are to add 1 to form the new exponent and divide by this new exponent.
Note: Dividing an expression by a fraction is the same as multiplying by the
reciprocal of that fraction:

5x^(-5)/(-5) - 4(3/5)x^(5/3) + C = \(\displaystyle . . . Next, I \ am \ switching \ over \ to \ Latex.\)


\(\displaystyle -1x^{-5} \ - \ \frac{12}{5}x^{\frac{5}{3}} \ + \ \bigg{C} \ = \\)


\(\displaystyle \frac{-1}{x^5} \ - \ \frac{12\sqrt[3]{x^5}}{5} \ + \ \bigg{C}\)