7.1 Integration By Parts/32

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - \int_{0}^{t} e^s \cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds}

$u=e^{s}~~~~~dv=\sin(t-s)dx~~~~~~~~~~~~~~~~u=e^{s}~~~~~dv=\cos(t-s)$

$du=e^{s}ds~~v=\cos(t-s)~~~~~~~~~~~~~~~~~~~du=e^{s}~~~~~v=-\sin(t-s)$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 2\int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot \cos(t-s) - e^s \cdot \sin(t-s)}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{t} e^s \sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(\cos(t-s) - \sin(t-s)) \Bigg|_0^t}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =\frac{e^t}{2}(\cos(0) - \sin(0)) -\frac{e^0}{2}(\cos(t) - \sin(t))}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =\frac{e^t}{2}-\frac{1}{2}(\cos(t) - \sin(t))}

1 2 3 4 5 7 8 9 10 11 12 13 14 15 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 43 45 47 48 49 50 51 52 53 54 61 65