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Apply the formula: $\sin\left(x^m\right)$$=\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\left(x^m\right)^{\left(2n+1\right)}$, where $x^m=t^2$, $x=t$ and $m=2$
Learn how to solve intégrales trigonométriques problems step by step online.
$\int\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\left(t^2\right)^{\left(2n+1\right)}dt$
Learn how to solve intégrales trigonométriques problems step by step online. int(sin(t^2))dt. Apply the formula: \sin\left(x^m\right)=\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\left(x^m\right)^{\left(2n+1\right)}, where x^m=t^2, x=t and m=2. Simplify \left(t^2\right)^{\left(2n+1\right)} 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+1. Apply the formula: x\left(a+b\right)=xa+xb, where a=2n, b=1, x=2 and a+b=2n+1. Apply the formula: \int\sum_{a}^{b} cxdx=\sum_{a}^{b} c\int xdx, where a=n=0, b=\infty , c=\frac{{\left(-1\right)}^n}{\left(2n+1\right)!} and x=t^{\left(4n+2\right)}.
