Esercizio
$\int x\left(x\cdot\cos\left(x^2\right)\right)dx$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the integral int(xxcos(x^2))dx. Applicare la formula: x\cdot x=x^2. Applicare la formula: \cos\left(x^m\right)=\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n\right)!}\left(x^m\right)^{2n}, dove x^m=x^2 e m=2. Simplify \left(x^2\right)^{2n} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2n. Applicare la formula: \sum_{a}^{b} xy=\sum_{a}^{b} yx, dove a=n=0, b=\infty , x=\frac{{\left(-1\right)}^n}{\left(2n\right)!}x^{4n} e y=x^2.
Find the integral int(xxcos(x^2))dx
Risposta finale al problema
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(3+4n\right)}}{\left(3+4n\right)\left(2n\right)!}+C_0$