Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nt^{\left(4n+3\right)}}{\left(4n+3\right)\left(2n+1\right)!}+C_0$
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Step-by-step Solution
Learn how to solve integration techniques problems step by step online. Solve the trigonometric integral int(sin(t^2))dt. Rewrite the function \sin\left(t^2\right) as it's representation in Maclaurin series expansion. 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. Solve the product 2\left(2n+1\right). We can rewrite the power series as the following.
Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nt^{\left(4n+3\right)}}{\left(4n+3\right)\left(2n+1\right)!}+C_0$
