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Popular Calculus Problems

integral of tan^3(2t)sec^4(2t)	\int\:\tan^{3}(2t)\sec^{4}(2t)dt
integral of 4/(x^2-8x+12)	\int\:\frac{4}{x^{2}-8x+12}dx
y^{''}+y^'-6y=4e^t,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y^{\prime\:}-6y=4e^{t},y(0)=0,y^{\prime\:}(0)=0
derivative of sqrt(x)+x^{-1/3}	derivative\:\sqrt{x}+x^{-\frac{1}{3}}
(\partial)/(\partial x)(3x^2y-3x+3y^3)	\frac{\partial\:}{\partial\:x}(3x^{2}y-3x+3y^{3})
integral of (x^2)/((x-1)(x-2))	\int\:\frac{x^{2}}{(x-1)(x-2)}dx
derivative of (3x^2-3x+1)x^3	derivative\:(3x^{2}-3x+1)x^{3}
integral of (x^3)/((1-x^4)^7)	\int\:\frac{x^{3}}{(1-x^{4})^{7}}dx
integral of cos(x)-sin(x)+sec^2(x)	\int\:\cos(x)-\sin(x)+\sec^{2}(x)dx
integral of 5z	\int\:5zdz
integral from 4 to infinity of e^{-3x}	\int\:_{4}^{\infty\:}e^{-3x}dx
(\partial)/(\partial x)(x/4)	\frac{\partial\:}{\partial\:x}(\frac{x}{4})
inverse oflaplace 5/(s(s+2))	inverselaplace\:\frac{5}{s(s+2)}
derivative of 524.8x^{0.75}	\frac{d}{dx}(524.8x^{0.75})
taylor (x^3-2x+4),2	taylor\:(x^{3}-2x+4),2
integral of (1/(2x^2-5x+7)+(2x+3)e^{2x})	\int\:(\frac{1}{2x^{2}-5x+7}+(2x+3)e^{2x})dx
derivative of sqrt(x)(x-4^2)	\frac{d}{dx}(\sqrt{x}(x-4)^{2})
(\partial)/(\partial x)(e^y+x+x^2+6)	\frac{\partial\:}{\partial\:x}(e^{y}+x+x^{2}+6)
tangent of f(x)=(x^2+5)/(x-5),\at x=3	tangent\:f(x)=\frac{x^{2}+5}{x-5},\at\:x=3
maclaurin cos(x/2)	maclaurin\:\cos(\frac{x}{2})
limit as x approaches 0+of (1+6x)^{3/x}	\lim\:_{x\to\:0+}((1+6x)^{\frac{3}{x}})
(\partial)/(\partial t)(arctan(xsqrt(t)))	\frac{\partial\:}{\partial\:t}(\arctan(x\sqrt{t}))
integral of cos(12x)	\int\:\cos(12x)dx
6x-8ysqrt(x^2+1)(dy)/(dx)=0	6x-8y\sqrt{x^{2}+1}\frac{dy}{dx}=0
limit as x approaches 1 of (1-\|x\|)/(x-1)	\lim\:_{x\to\:1}(\frac{1-\left\|x\right\|}{x-1})
derivative of 20x^{1/2}-1/2 x^{20}	\frac{d}{dx}(20x^{\frac{1}{2}}-\frac{1}{2}x^{20})
integral of (sin^7(6x))/(cos^4(6x))	\int\:\frac{\sin^{7}(6x)}{\cos^{4}(6x)}dx
limit as x approaches 2.9 of x^2+3x	\lim\:_{x\to\:2.9}(x^{2}+3x)
derivative of y=(2t)/(3+t^2)	derivative\:y=\frac{2t}{3+t^{2}}
limit as x approaches-1 of x^2+1	\lim\:_{x\to\:-1}(x^{2}+1)
(\partial)/(\partial y)(e^{xy}x)	\frac{\partial\:}{\partial\:y}(e^{xy}x)
slope of ((-10x-9yx^2))/(3(x^3-5y^2))	slope\:\frac{(-10x-9yx^{2})}{3(x^{3}-5y^{2})}
integral of x*cos(2x)	\int\:x\cdot\:\cos(2x)dx
integral of (ln(v))/(v^2+2v+1)	\int\:\frac{\ln(v)}{v^{2}+2v+1}dv
tangent of x^4+9x^2-x(1.9)	tangent\:x^{4}+9x^{2}-x(1.9)
tangent of f(x)=x^2+2,\at x=-1	tangent\:f(x)=x^{2}+2,\at\:x=-1
d/(dt)(1/(sqrt(1+4t^2)))	\frac{d}{dt}(\frac{1}{\sqrt{1+4t^{2}}})
(\partial)/(\partial x)((xe^y)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{xe^{y}}{x+y})
limit as x approaches 1 of 2^{1/(x-1)}	\lim\:_{x\to\:1}(2^{\frac{1}{x-1}})
integral of (x+6)/((x+2)^2)	\int\:\frac{x+6}{(x+2)^{2}}dx
derivative of insin(x)	\frac{d}{dx}(in\sin(x))
(\partial)/(\partial x)(3x^4-65x^3)	\frac{\partial\:}{\partial\:x}(3x^{4}-65x^{3})
integral from 0 to pi/6 of cos(3x)	\int\:_{0}^{\frac{π}{6}}\cos(3x)dx
y^{''}+y=cos(t),y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y=\cos(t),y(0)=0,y^{\prime\:}(0)=0
limit as x approaches-3+of ln(x+3)	\lim\:_{x\to\:-3+}(\ln(x+3))
(4x^2-y^2)dx-xydy=0	(4x^{2}-y^{2})dx-xydy=0
y^'=2(2x+y)^2	y^{\prime\:}=2(2x+y)^{2}
derivative of 13xe^{-x}	\frac{d}{dx}(13xe^{-x})
(\partial)/(\partial v)(1/4 (u-v))	\frac{\partial\:}{\partial\:v}(\frac{1}{4}(u-v))
derivative of f(x)=(x-1)^2	derivative\:f(x)=(x-1)^{2}
sum from n=1 to infinity of e^{1/n}	\sum\:_{n=1}^{\infty\:}e^{\frac{1}{n}}
limit as x approaches 0 of 1+sqrt(x)	\lim\:_{x\to\:0}(1+\sqrt{x})
tangent of y=8x^{1/2}+8x^{3/2}+6,\at x=4	tangent\:y=8x^{\frac{1}{2}}+8x^{\frac{3}{2}}+6,\at\:x=4
integral of sqrt((2+x)/(2-x))	\int\:\sqrt{\frac{2+x}{2-x}}dx
(\partial)/(\partial x)(1/(2x^{1/2)})	\frac{\partial\:}{\partial\:x}(\frac{1}{2x^{\frac{1}{2}}})
derivative of y=20sqrt(x)	derivative\:y=20\sqrt{x}
y^{'''}-2y^{''}-y+2y=0	y^{\prime\:\prime\:\prime\:}-2y^{\prime\:\prime\:}-y+2y=0
limit as x approaches 0 of (3x^2-8x)/x	\lim\:_{x\to\:0}(\frac{3x^{2}-8x}{x})
f(x)=(7+2ln(x))/x	f(x)=\frac{7+2\ln(x)}{x}
tangent of f(x)=x^2-6,(-2,-2)	tangent\:f(x)=x^{2}-6,(-2,-2)
derivative of asin(x+bcos(x))	\frac{d}{dx}(a\cdot\:\sin(x)+b\cdot\:\cos(x))
limit as x approaches 9 of 5+x^2	\lim\:_{x\to\:9}(5+x^{2})
integral from 0 to 8 of 1/(sqrt(64-x^2))	\int\:_{0}^{8}\frac{1}{\sqrt{64-x^{2}}}dx
derivative of e^{3x}sin(3x)	\frac{d}{dx}(e^{3x}\sin(3x))
limit as x approaches infinity of x^2-2	\lim\:_{x\to\:\infty\:}(x^{2}-2)
integral of y^{2/3}	\int\:y^{\frac{2}{3}}dy
derivative of x^{ln(3x})	\frac{d}{dx}(x^{\ln(3x)})
integral of 25/27 sin^2(x)	\int\:\frac{25}{27}\sin^{2}(x)dx
derivative of 6sec(x-12cos(x))	\frac{d}{dx}(6\sec(x)-12\cos(x))
y^'+ycos(t)= 1/2 sin(2t)	y^{\prime\:}+y\cos(t)=\frac{1}{2}\sin(2t)
(d^2)/(dx^2)(x^6e^x)	\frac{d^{2}}{dx^{2}}(x^{6}e^{x})
integral from 0 to 1 of 7	\int\:_{0}^{1}7
(\partial)/(\partial x)((x+{v}(x,t)t)^3)	\frac{\partial\:}{\partial\:x}((x+{v}(x,t)t)^{3})
limit as x approaches-3 of-x^2+6x-1	\lim\:_{x\to\:-3}(-x^{2}+6x-1)
sum from n=1 to infinity of 8/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{8}{5^{n}}
derivative of (4x^2-7x+6/(3x+5))	\frac{d}{dx}(\frac{4x^{2}-7x+6}{3x+5})
xy^'=y+x^2sin(x)	xy^{\prime\:}=y+x^{2}\sin(x)
derivative of e^xx^2+2xe^x	\frac{d}{dx}(e^{x}x^{2}+2xe^{x})
integral of 1/(sqrt(529+x^2))	\int\:\frac{1}{\sqrt{529+x^{2}}}dx
derivative of 9ln(x)	\frac{d}{dx}(9\ln(x))
derivative of 11e^x	derivative\:11e^{x}
integral of 1/2 x^{1/2}	\int\:\frac{1}{2}x^{\frac{1}{2}}dx
limit as x approaches 4 of x^2-3x+7	\lim\:_{x\to\:4}(x^{2}-3x+7)
limit as x approaches 3 of 0	\lim\:_{x\to\:3}(0)
derivative of ln(ln(9s))	derivative\:\ln(\ln(9s))
derivative of-t^2+2t+4	derivative\:-t^{2}+2t+4
(dy)/(dx)= 1/(sqrt(1+x^2))	\frac{dy}{dx}=\frac{1}{\sqrt{1+x^{2}}}
inverse oflaplace (5s)/(s^2+4s+5)	inverselaplace\:\frac{5s}{s^{2}+4s+5}
(2y+2t-9)dt+(4y+2t-1)dy=0	(2y+2t-9)dt+(4y+2t-1)dy=0
integral of (3-x)^2	\int\:(3-x)^{2}dx
f'(x)=f(x)(1-f(x))	f\prime\:(x)=f(x)(1-f(x))
d/(dt)(2t^3)	\frac{d}{dt}(2t^{3})
(d^3)/(dx^3)(sqrt(4x+8))	\frac{d^{3}}{dx^{3}}(\sqrt{4x+8})
derivative of y=(2x^5+6)/(x^3)	derivative\:y=\frac{2x^{5}+6}{x^{3}}
integral from 0 to 5 of sqrt(5x)	\int\:_{0}^{5}\sqrt{5x}dx
tangent of y=sqrt(x),(64,8)	tangent\:y=\sqrt{x},(64,8)
inverse oflaplace (12s)/(12s-30s^2)	inverselaplace\:\frac{12s}{12s-30s^{2}}
(dy)/(dx)=((e^y))/(xy)	\frac{dy}{dx}=\frac{(e^{y})}{xy}
derivative of (1-5t)/(4+t)	derivative\:\frac{1-5t}{4+t}
integral of sin(8x)cos(8x)	\int\:\sin(8x)\cos(8x)dx

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