Sr Examen
Integral de (sqrt(1+2x))/(4x+3) dx
Solución
Ha introducido
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1 / | | _________ | \/ 1 + 2*x | ----------- dx | 4*x + 3 | / 4
$$\int\limits_{4}^{1} \frac{\sqrt{2 x + 1}}{4 x + 3}\, dx$$
Integral(sqrt(1 + 2*x)/(4*x + 3), (x, 4, 1))
Respuesta (Indefinida)
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/ | | _________ _________ ___ / ___ _________\ | \/ 1 + 2*x \/ 1 + 2*x \/ 2 *atan\\/ 2 *\/ 1 + 2*x / | ----------- dx = C + ----------- - ----------------------------- | 4*x + 3 2 4 | /
$$\int \frac{\sqrt{2 x + 1}}{4 x + 3}\, dx = C + \frac{\sqrt{2 x + 1}}{2} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{2 x + 1} \right)}}{4}$$
Gráfica
Respuesta
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/ ____\ / ___\
___ |\/ 19 | ___ |\/ 7 |
___ \/ 2 *asin|------| \/ 2 *asin|-----|
3 \/ 3 \ 19 / \ 7 /
- - + ----- - ------------------ + -----------------
2 2 4 4
$$- \frac{3}{2} - \frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{19}}{19} \right)}}{4} + \frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{7}}{7} \right)}}{4} + \frac{\sqrt{3}}{2}$$
=
=
/ ____\ / ___\
___ |\/ 19 | ___ |\/ 7 |
___ \/ 2 *asin|------| \/ 2 *asin|-----|
3 \/ 3 \ 19 / \ 7 /
- - + ----- - ------------------ + -----------------
2 2 4 4
$$- \frac{3}{2} - \frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{19}}{19} \right)}}{4} + \frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{7}}{7} \right)}}{4} + \frac{\sqrt{3}}{2}$$
-3/2 + sqrt(3)/2 - sqrt(2)*asin(sqrt(19)/19)/4 + sqrt(2)*asin(sqrt(7)/7)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.