Esercizio
$\int_{\sqrt{y}}^2ycosx^5dx$
Soluzione passo-passo
Impara online a risolvere i problemi di integrali trigonometrici passo dopo passo. int(ycos(x)^5)dx&y^(1/2)&2. Applicare la formula: \int_{a}^{b} cxdx=c\int_{a}^{b} xdx, dove a=\sqrt{y}, b=2, c=y e x=\cos\left(x\right)^5. Applicare la formula: \int\cos\left(\theta \right)^ndx=\frac{\cos\left(\theta \right)^{\left(n-1\right)}\sin\left(\theta \right)}{n}+\frac{n-1}{n}\int\cos\left(\theta \right)^{\left(n-2\right)}dx, dove n=5. Applicare la formula: \int\cos\left(\theta \right)^ndx=\frac{\cos\left(\theta \right)^{\left(n-1\right)}\sin\left(\theta \right)}{n}+\frac{n-1}{n}\int\cos\left(\theta \right)^{\left(n-2\right)}dx, dove n=3. Applicare la formula: x\left(a+b\right)=xa+xb, dove a=\frac{\cos\left(x\right)^{2}\sin\left(x\right)}{3}, b=\frac{2}{3}\int\cos\left(x\right)dx, x=\frac{4}{5} e a+b=\frac{\cos\left(x\right)^{2}\sin\left(x\right)}{3}+\frac{2}{3}\int\cos\left(x\right)dx.
int(ycos(x)^5)dx&y^(1/2)&2
Risposta finale al problema
$y\left(\frac{\cos\left(2\right)^{4}\sin\left(2\right)}{5}+\frac{4\cdot \cos\left(2\right)^{2}\sin\left(2\right)}{15}+\frac{8}{15}\sin\left(2\right)-\left(\frac{\cos\left(\sqrt{y}\right)^{4}\sin\left(\sqrt{y}\right)}{5}+\frac{4\cos\left(\sqrt{y}\right)^{2}\sin\left(\sqrt{y}\right)}{15}+\frac{8}{15}\sin\left(\sqrt{y}\right)\right)\right)$