# Trouble differentiating $\int_1^{x^3}\arcsin(t)dt$

I'm having trouble with an integral problem which goes like this: Differentiate $$\int_1^{x^3}\arcsin(t)dt$$

The rule I know would be that you make $t$ equal to $x^3$ and then use the chain rule to achieve: $$3x^2\arcsin(x^3)$$

But the answer says that it is actually: $$3x^2\arcsin(3x^3)$$

Why is this?

• You are totally correct ! One more typo in a textbook. – Claude Leibovici Jun 21 '15 at 7:37
• Brilliant! Thank you Claude, this makes me a happy man :) – Dave Jun 21 '15 at 7:42
• You are brilliant ! I did not do anything. Cheers :-) – Claude Leibovici Jun 21 '15 at 7:44

$$\frac{d}{dx} \int_c^{g(x)} f(t) dt=g'(x) f(g(x))$$