Question

\int xcos ax2dx with respect to x

A cos3x+c

B sin2x+c

C sec2x+1

D 12asinax2+c

Answer 1

Question #50926– Math – Integral Calculus

$$\int x \cos a x ^ {2} d x$$

**Solution:**

Let $x^{2} = t$, then $2xdx = dt$

Hence:

$$\begin{array}{l} \int x \cos a x ^ {2} d x = \frac {1}{2} \int \cos a x ^ {2} \cdot 2 x d x = \frac {1}{2} \int \cos a t d t = \\ = \frac {1}{2 a} \sin a t + C = \frac {1}{2 a} \sin a x ^ {2} + C \end{array}$$

**Answer:**

$$D: \frac {1}{2 a} \sin a x ^ {2} + C$$

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