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<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal">Integral Practice Problems.  To see the solution, place the cursor on the</Text-field>
<Text-field style="Normal" layout="Normal">appropriate line and press &quot;enter&quot;:</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans1:=int((2*x^2-x+4)/(x^3+4*x),x);</Text-field>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans2:=int(exp(2*theta)*sin(3*theta),theta);</Text-field>
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<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans3:=int(1/(y*(2-y)),y);</Text-field>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans4:=int(t^2*cos(3*t),t);</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans5:=int(x^3*exp(x^2),x);</Text-field>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans6:=int(x*5^x,x);</Text-field>
</Input>
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<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans7:=int((x-1)/(x^2+1),x);</Text-field>
</Input>
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<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">For Problem 8, Maple will give an inverse hyperbolic arc tangent.  To verify</Text-field>
<Text-field style="Text" layout="Normal">your solution, here is the integral using the substitution:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ans8:=int(1/((u+1)*(u-1)),u);</Text-field>
</Input>
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<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(u=sqrt(x+1),Ans8);</Text-field>
</Input>
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<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="Ans9 := int(y*sinh(y), y); 1" display="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">QyQ+SSVBbnM5RzYiLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJkkieUdGJSIiIi1JJXNpbmhHRiU2I0YtRi5GLUYu</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="Ans10 := int(1/(x^4-x^2), x); 1" display="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">QyQ+SSZBbnMxMEc2Ii1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiQsJiokSSJ4R0YlIiIlIiIiKiRGLyIiIyEiIkY0Ri9GMQ==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="Ans11 := int(t^2/(t+4), t); 1" display="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">QyQ+SSZBbnMxMUc2Ii1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiZJInRHRiUiIiMsJkYtIiIiIiIlRjAhIiJGLUYw</Equation></Text-field>
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<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="Ans12 := int(cos(ln(x)), x); 1" display="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">QyQ+SSZBbnMxMkc2Ii1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUkkY29zR0YoNiMtSSNsbkdGKDYjSSJ4R0YlRjIiIiI=</Equation></Text-field>
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<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="Ans13 := int((x-1)/(x+4), x); 1" display="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">QyQ+SSZBbnMxM0c2Ii1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYsJkkieEdGJSIiIiEiIkYvRi8sJkYuRi8iIiVGL0YwRi5GLw==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="Ans14 := int(arctan(x), x); 1" display="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">QyQ+SSZBbnMxNEc2Ii1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUknYXJjdGFuR0YoNiNJInhHRiVGLyIiIg==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn</Equation></Text-field>
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