Sr Examen
Integral de (3x+2)arctg(5x+7) dx
Solución
Ha introducido
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1 / | | (3*x + 2)*atan(5*x + 7) dx | / 0
$$\int\limits_{0}^{1} \left(3 x + 2\right) \operatorname{atan}{\left(5 x + 7 \right)}\, dx$$
Integral((3*x + 2)*atan(5*x + 7), (x, 0, 1))
Respuesta (Indefinida)
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/ / 2\ / 2 \ 2 | 72*atan(7 + 5*x) 3*x log\1 + (7 + 5*x) / 21*log\10 + 5*x + 14*x/ 2*(7 + 5*x)*atan(7 + 5*x) 3*x *atan(7 + 5*x) | (3*x + 2)*atan(5*x + 7) dx = C - ---------------- - --- - ------------------- + ------------------------ + ------------------------- + ------------------ | 25 10 5 50 5 2 /
$$\int \left(3 x + 2\right) \operatorname{atan}{\left(5 x + 7 \right)}\, dx = C + \frac{3 x^{2} \operatorname{atan}{\left(5 x + 7 \right)}}{2} - \frac{3 x}{10} + \frac{2 \left(5 x + 7\right) \operatorname{atan}{\left(5 x + 7 \right)}}{5} - \frac{\log{\left(\left(5 x + 7\right)^{2} + 1 \right)}}{5} + \frac{21 \log{\left(5 x^{2} + 14 x + 10 \right)}}{50} - \frac{72 \operatorname{atan}{\left(5 x + 7 \right)}}{25}$$
Gráfica
Respuesta
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3 11*log(10) 2*atan(7) 11*log(29) 171*atan(12) - -- - ---------- + --------- + ---------- + ------------ 10 50 25 50 50
$$- \frac{11 \log{\left(10 \right)}}{50} - \frac{3}{10} + \frac{2 \operatorname{atan}{\left(7 \right)}}{25} + \frac{11 \log{\left(29 \right)}}{50} + \frac{171 \operatorname{atan}{\left(12 \right)}}{50}$$
=
=
3 11*log(10) 2*atan(7) 11*log(29) 171*atan(12) - -- - ---------- + --------- + ---------- + ------------ 10 50 25 50 50
$$- \frac{11 \log{\left(10 \right)}}{50} - \frac{3}{10} + \frac{2 \operatorname{atan}{\left(7 \right)}}{25} + \frac{11 \log{\left(29 \right)}}{50} + \frac{171 \operatorname{atan}{\left(12 \right)}}{50}$$
-3/10 - 11*log(10)/50 + 2*atan(7)/25 + 11*log(29)/50 + 171*atan(12)/50
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.