DLMF:4.26.E7 (Q1823)

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DLMF:4.26.E7
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    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
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    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
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
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