DLMF:4.26.E7 (Q1823): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3afdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11221 / rank
 
Normal rank
Property / Symbols used: Q11221 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11221 / qualifier
 
xml-id: C4.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1fdec

Latest revision as of 18:41, 1 January 2020

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DLMF:4.26.E7
No description defined

    Statements

    Defining formula
    ∫ e a ⁢ x ⁢ sin ⁡ ( b ⁢ x ) ⁢ d x = e a ⁢ x a 2 + b 2 ⁢ ( a ⁢ sin ⁡ ( b ⁢ x ) - b ⁢ cos ⁡ ( b ⁢ x ) ) , superscript 𝑒 𝑎 𝑥 𝑏 𝑥 𝑥 superscript 𝑒 𝑎 𝑥 superscript 𝑎 2 superscript 𝑏 2 𝑎 𝑏 𝑥 𝑏 𝑏 𝑥 {\displaystyle{\displaystyle\int e^{ax}\sin\left(bx\right)\mathrm{d}x=\frac{e^% {ax}}{a^{2}+b^{2}}(a\sin\left(bx\right)-b\cos\left(bx\right)),}}
    0 references
    DLMF id
    DLMF:4.26.E7
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
    0 references
    Q11221
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1dec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1fdec
    0 references
     
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