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Math Help - Integration Problems

  1. #1
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    Integration Problems

    I've got the following problems and have just learned latex especially in the hope that someone can help me! I'm struggling a bit with this.

    1]  \int \displaystyle{\frac{1}{x}} + x^-3  (dx)

    2]  \int \displaystyle{\frac{x^2 + x}{x}} (dx)

    3]  \int 2\sqrt{x} - \displaystyle{\frac{3}{x^3}} (dx)

    4]  \int \sqrt{x} - \displaystyle{\frac{2}{x^2}} (dx)

    5]  \int \displaystyle{\frac{4}{x^3}} - ^7\sqrt{x} (dx)

    Here are the answers to a few I could come up with:

    1]  \displaystyle{\frac{1}{x^3}} - \displaystyle{\frac{1}{x}} + c

    2]  \displaystyle{\frac{x^3}{3}} + \displaystyle{\frac{x^2}{2}} + c

    3]  \displaystyle{\frac{4x^3/2}{3}} + \displaystyle{\frac{3}{x}} + c

    This is all I could do can you please help with the rest? It's the first time I've done latex as I say so I'm sorry if it's unreadable.
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  2. #2
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    Quote Originally Posted by db5vry View Post
    I've got the following problems and have just learned latex especially in the hope that someone can help me! I'm struggling a bit with this.

    1]  \int \displaystyle{\frac{1}{x}} + x^-3 (dx)

    2]  \int \displaystyle{\frac{x^2 + x}{x}} (dx)

    3]  \int 2\sqrt{x} - \displaystyle{\frac{3}{x^3}} (dx)

    4]  \int \sqrt{x} - \displaystyle{\frac{2}{x^2}} (dx)

    5]  \int \displaystyle{\frac{4}{x^3}} - ^7\sqrt{x} (dx)

    Here are the answers to a few I could come up with:

    1]  \displaystyle{\frac{1}{x^3}} - \displaystyle{\frac{1}{x}} + c

    2]  \displaystyle{\frac{x^3}{3}} + \displaystyle{\frac{x^2}{2}} + c

    3]  \displaystyle{\frac{4x^3/2}{3}} + \displaystyle{\frac{3}{x}} + c

    This is all I could do can you please help with the rest? It's the first time I've done latex as I say so I'm sorry if it's unreadable.
    These are the standard integration rules


    \int x^n\, dx = \frac{x^{n+1}}{n+1} + c,\;\;\;n \ne -1
    \int \frac{1}{x}\, dx = \ln |\,x\,| + c,
    \int c f\,dx = c\int f\,dx
    \int f+g\, dx = \int f\,dx + \int g\,dx

    so for example the fifth question

    \int \frac{4}{x^3} - \sqrt[7]{x} \;dx\;=\; 4 \int x^{-3}\, dx - \int x^{\frac{1}{7}} \;dx = 4 \frac{x^{-2}}{-2} - \frac{x^{\frac{8}{7}}}{\frac{8}{7}} + c = -\frac{2}{x^2} - \frac{7}{8} x^{\frac{8}{7}} + c

    You try the rest (expand #2 first).
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