Find \int\ x\ cos(x^2+3)dx


Find {eq}\int\ x\ cos(x^2+3)dx {/eq}


The process of finding a function, given its derivative, is called anti-differentiation (or integration). If F'(x) = f(x), we say F(x) is an anti-derivative of f(x).

Answer and Explanation:

{eq}\int\ x\ cos(x^2+3)dx {/eq}

Put {eq}x^2+3 = u\\ 2xdx=du {/eq}

{eq}\int \frac{1}{2} \cos(u) du\\ =\frac{1}{2} \sin(u) +c \\ =\frac{1}{2} \sin(x^2+3) +c {/eq}

Learn more about this topic:

Integration Problems in Calculus: Solutions & Examples

from AP Calculus AB & BC: Homework Help Resource

Chapter 13 / Lesson 13

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