I have another rather simple problem that I cannot seem to be able to solve. I cannot find the right substitution.
The problem is:
$$\int\frac{\sin^3{x}}{\sqrt{\cos{x}}}dx$$
I would appreciate any help...
Thank you in advance!
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Sign up to join this communityI have another rather simple problem that I cannot seem to be able to solve. I cannot find the right substitution.
The problem is:
$$\int\frac{\sin^3{x}}{\sqrt{\cos{x}}}dx$$
I would appreciate any help...
Thank you in advance!
HINT:
Use a substitution $\text{u}=\cos\left(x\right)$ then the integrand changes to $-\frac{1-\text{u}^2}{\sqrt{\text{u}}}$ then substitute $\text{s}:=\sqrt{\text{u}}$ then the integrand changes to $-2\cdot\left(1-\text{s}^4\right)$
Put $cosx=z^2$ then $$\int\frac{\sin^3{x}}{\sqrt{\cos{x}}}dx=\int2(z^4-1)dz.$$