Solve Integral 17(sin(x))^3(cos(x))^9

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Homework Statement



Integral 17(sin(x))^3(cos(x))^9

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Homework Equations


Integration


The Attempt at a Solution


I get (-17(5sin(x))^2 +1)(cos(x))^10)/60. But I'm wrong. It says I need to change something but I don't know what.
 
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substitute for cosx. then you will see that one of the sinx goes out with the change of integration variable. then you should be able to solve it easily
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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