Sr Examen
Integral de x^2dx/(5x^4+7)^5 dx
Solución
Ha introducido
[src]
1 / | | 2 | x | ----------- dx | 5 | / 4 \ | \5*x + 7/ | / 0
$$\int\limits_{0}^{1} \frac{x^{2}}{\left(5 x^{4} + 7\right)^{5}}\, dx$$
Integral(x^2/(5*x^4 + 7)^5, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ 4 ______\ / ___ 4 ______\ / ____ ___ 3/4 4 ___\ / ____ ___ 3/4 4 ___\ | ___ 4 ______ | x*\/ 2 *\/ 1715 | ___ 4 ______ | x*\/ 2 *\/ 1715 | ___ 4 ___ 3/4 | 2 \/ 35 x*\/ 2 *5 *\/ 7 | ___ 4 ___ 3/4 | 2 \/ 35 x*\/ 2 *5 *\/ 7 | | 2 15 11 3 7 39*\/ 2 *\/ 1715 *atan|1 + ----------------| 39*\/ 2 *\/ 1715 *atan|-1 + ----------------| 39*\/ 2 *\/ 5 *7 *log|x + ------ + ------------------| 39*\/ 2 *\/ 5 *7 *log|x + ------ - ------------------| | x 73125*x + 389025*x + 635579*x + 761215*x \ 7 / \ 7 / \ 5 5 / \ 5 5 / | ----------- dx = C + ---------------------------------------------------------------------------------- + -------------------------------------------- + --------------------------------------------- - --------------------------------------------------------- + --------------------------------------------------------- | 5 16 12 4 8 137682944 137682944 275365888 275365888 | / 4 \ 35418937344 + 9219840000*x + 51631104000*x + 101196963840*x + 108425318400*x | \5*x + 7/ | /
$$\int \frac{x^{2}}{\left(5 x^{4} + 7\right)^{5}}\, dx = C + \frac{73125 x^{15} + 389025 x^{11} + 761215 x^{7} + 635579 x^{3}}{9219840000 x^{16} + 51631104000 x^{12} + 108425318400 x^{8} + 101196963840 x^{4} + 35418937344} + \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(x^{2} - \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7} x}{5} + \frac{\sqrt{35}}{5} \right)}}{275365888} - \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(x^{2} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7} x}{5} + \frac{\sqrt{35}}{5} \right)}}{275365888} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt[4]{1715} \sqrt{2} x}{7} - 1 \right)}}{137682944} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt[4]{1715} \sqrt{2} x}{7} + 1 \right)}}{137682944}$$
Gráfica
Respuesta
[src]
/ ___ 4 ______\ / ___ 4 ______\ / ____ ___ 3/4 4 ___\ / ____ ___ 3/4 4 ___\
___ 4 ______ | \/ 2 *\/ 1715 | ___ 4 ______ | \/ 2 *\/ 1715 | ___ 4 ___ 3/4 | \/ 35 \/ 2 *5 *\/ 7 | ___ 4 ___ 3/4 | \/ 35 \/ 2 *5 *\/ 7 |
39*\/ 2 *\/ 1715 *atan|1 - --------------| 39*\/ 2 *\/ 1715 *atan|1 + --------------| 39*\/ 2 *\/ 5 *7 *log|1 + ------ + ----------------| 39*\/ 2 *\/ 5 *7 *log|1 + ------ - ----------------|
4841 \ 7 / \ 7 / \ 5 5 / \ 5 5 /
--------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------------------ + ------------------------------------------------------
796594176 137682944 137682944 275365888 275365888
$$- \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(1 + \frac{\sqrt{35}}{5} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} \right)}}{275365888} + \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(- \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} + 1 + \frac{\sqrt{35}}{5} \right)}}{275365888} - \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(- \frac{\sqrt[4]{1715} \sqrt{2}}{7} + 1 \right)}}{137682944} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(1 + \frac{\sqrt[4]{1715} \sqrt{2}}{7} \right)}}{137682944} + \frac{4841}{796594176}$$
=
=
/ ___ 4 ______\ / ___ 4 ______\ / ____ ___ 3/4 4 ___\ / ____ ___ 3/4 4 ___\
___ 4 ______ | \/ 2 *\/ 1715 | ___ 4 ______ | \/ 2 *\/ 1715 | ___ 4 ___ 3/4 | \/ 35 \/ 2 *5 *\/ 7 | ___ 4 ___ 3/4 | \/ 35 \/ 2 *5 *\/ 7 |
39*\/ 2 *\/ 1715 *atan|1 - --------------| 39*\/ 2 *\/ 1715 *atan|1 + --------------| 39*\/ 2 *\/ 5 *7 *log|1 + ------ + ----------------| 39*\/ 2 *\/ 5 *7 *log|1 + ------ - ----------------|
4841 \ 7 / \ 7 / \ 5 5 / \ 5 5 /
--------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------------------ + ------------------------------------------------------
796594176 137682944 137682944 275365888 275365888
$$- \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(1 + \frac{\sqrt{35}}{5} + \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} \right)}}{275365888} + \frac{39 \sqrt{2} \sqrt[4]{5} \cdot 7^{\frac{3}{4}} \log{\left(- \frac{\sqrt{2} \cdot 5^{\frac{3}{4}} \sqrt[4]{7}}{5} + 1 + \frac{\sqrt{35}}{5} \right)}}{275365888} - \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(- \frac{\sqrt[4]{1715} \sqrt{2}}{7} + 1 \right)}}{137682944} + \frac{39 \sqrt[4]{1715} \sqrt{2} \operatorname{atan}{\left(1 + \frac{\sqrt[4]{1715} \sqrt{2}}{7} \right)}}{137682944} + \frac{4841}{796594176}$$
4841/796594176 - 39*sqrt(2)*1715^(1/4)*atan(1 - sqrt(2)*1715^(1/4)/7)/137682944 + 39*sqrt(2)*1715^(1/4)*atan(1 + sqrt(2)*1715^(1/4)/7)/137682944 - 39*sqrt(2)*5^(1/4)*7^(3/4)*log(1 + sqrt(35)/5 + sqrt(2)*5^(3/4)*7^(1/4)/5)/275365888 + 39*sqrt(2)*5^(1/4)*7^(3/4)*log(1 + sqrt(35)/5 - sqrt(2)*5^(3/4)*7^(1/4)/5)/275365888
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.