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mypetispig83
mypetispig83 asked in Science & MathematicsMathematics · 1 decade ago

How to integrate this _ INT e^(x) * 10^(x) dx ?

[e^(x) 10^(x)] / ln 10 + C

3 Answers

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  • Hemant
    Lv 7
    1 decade ago
    Favorite Answer

    Easiest Solution

    ▬▬▬▬▬▬▬▬

    I = ∫ (e^x).(10^x) dx

    ..= ∫ ( 10e )^x dx

    ..= (10e)^x / ( ln 10e ) + C

    ..= (10^x)(e^x) / ( 1 + ln 10 ) + C ... Ans.

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    Happy To Help !

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  • Ed I
    Lv 7
    1 decade ago

    ∫ e^x 10^x dx = ∫ e^x e^(x ln 10) dx = ∫ e^(x + x ln 10) dx

    Let u = x + x ln 10

    then du = (1 + ln 10) dx

    So now we have 1/(1 + ln 10) ∫ e^u du = 1/(1 + ln 10) e^u + C = 1/(1 + ln 10) e^(x + x ln 10) + C = 1/(1 + ln 10) e^x 10^x + C

    Source(s): I have taught math for over 40 yr, including 18 yr of AP Calc.
  • cidyah
    Lv 7
    1 decade ago

    Let z = ∫ e^x 10^x dx

    Integrate by parts

    dv=e^x

    v=e^x

    u=10^x

    du=10^x ln(10)

    ∫ u dv = uv - ∫ vdu

    10^x e^x - ∫ e^x 10^x ln(10) dx

    z= 10^x e^x - ln(10) z

    z(1+ln(10)) = 10^x e^x

    z = 10^x e^x / (1+ln(10)) + C

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