U-Substitution Practice

\[\int (1-2x)^5 \, dx\]

\[\int \frac{x}{x+1} \, dx\]

\[\int x \, \cos (1+x^2) \, dx\]

\[\int \frac{x^2}{1+x^3} \, dx\]

\[\int \frac{x^2-4}{x^3-12x+6} \, dx\]

\[\int \sin^4(\theta) \cos(\theta)\, d\theta\]

\[\int \cot \theta \, d\theta\]

\[\int \tan x \, dx\]

\[\int \frac{(\ln x)^4}{4x} \, dx\]

\[\int \frac{\sin (\ln x)}{x} \, dx\]

\[\int x^2 \cos (x^3) \, dx\]

\[\int (t-2)\sqrt{3t^2-12t} \, dt\]

\[\int \left(1-\frac{1}{x}\right)\, \sin\left(x - \ln x \right) \, dx\]

\[\int_0^1 \frac{e^z+25}{e^z+25z} \, dz\]

\[\int e^{x^5} x^4 \, dx\]

\[\int \frac{x^8}{\sqrt{x^9-7}} \, dx\]

\[\int \frac{e^{5x}}{2+e^{5x}} \, dx\]

\[\int \frac{1}{x \ln x} \, dx\]

\[\int x \, \sqrt{1-x^2} \, dx\]

\[\int \sin \theta \, (1+ \cos \theta)^3 \, d\theta\]

\[\int_{e^{16}}^{e^{81}} \frac{dx}{x\sqrt{\ln(x)}}\]

\[\int \sin(t) \sqrt{1+\cos(t)}\, dt\]

\[\int_{-1}^1 x\,(x^2+1)^2 \, dx\]

\[\int_0^1 x \, \sqrt{5x^2+4} \, dx\]

\[\int_1^2 \frac{x}{(x^2+3)^2} \, dx\]

\[\int_0^1 \frac{x+2}{\sqrt{x^2+4x}} \, dx\]

\[\int_0^4 \frac{e^{\sqrt{x}}}{\sqrt{x}} \, dx\]

\[\int_0^1 \frac{\tan^{-1} t}{1+t^2} \, dt\]

\[\int \frac{x^3}{(1+x^2)^2} \, dx\]

\[\int e^{\cos(2t)}\sin(2t) \, dt\]