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Popular Calculus Problems

integral of sin^2(θ)cos^3(θ)	\int\:\sin^{2}(θ)\cos^{3}(θ)dθ
tangent of y=(10x^2-6x+3)(1+2x),\at x=1	tangent\:y=(10x^{2}-6x+3)(1+2x),\at\:x=1
integral of (x^2)/((1-x^2)^{3/2)}	\int\:\frac{x^{2}}{(1-x^{2})^{\frac{3}{2}}}dx
integral of (8x^4+5)^332x^3	\int\:(8x^{4}+5)^{3}32x^{3}dx
derivative of 7/(sqrt(x+2))	\frac{d}{dx}(\frac{7}{\sqrt{x+2}})
tangent of (2x+1)/(x+2),\at a=1	tangent\:\frac{2x+1}{x+2},\at\:a=1
integral of (x^2)/(7-x^3)	\int\:\frac{x^{2}}{7-x^{3}}dx
integral of 8/(1+9x^2)	\int\:\frac{8}{1+9x^{2}}dx
limit as x approaches 0 of (tan(x)+x)/x	\lim\:_{x\to\:0}(\frac{\tan(x)+x}{x})
sum from n=0 to infinity of 3(-1/4)^{n-1}	\sum\:_{n=0}^{\infty\:}3(-\frac{1}{4})^{n-1}
integral of 20e^x	\int\:20e^{x}dx
derivative of (12/(x^4))	\frac{d}{dx}(\frac{12}{x^{4}})
limit as (x,y) approaches (0,0) of xy^8	\lim\:_{(x,y)\to\:(0,0)}(xy^{8})
derivative of 1/(x^2+c)	\frac{d}{dx}(\frac{1}{x^{2}+c})
derivative of (1-2x^{1/x})	\frac{d}{dx}((1-2x)^{\frac{1}{x}})
limit as x approaches 0+of xe^{-2/x}	\lim\:_{x\to\:0+}(xe^{-\frac{2}{x}})
y^'+2ty=e^{-t^2}	y^{\prime\:}+2ty=e^{-t^{2}}
integral from 0 to pi of 6cos^2(3x)	\int\:_{0}^{π}6\cos^{2}(3x)dx
integral of (x^2-4x+5)^2	\int\:(x^{2}-4x+5)^{2}dx
derivative of (x+2)^{2/3}	derivative\:(x+2)^{\frac{2}{3}}
tangent of y=((x-2))/((x-3))	tangent\:y=\frac{(x-2)}{(x-3)}
laplacetransform 6e^{5t}cos(2t)-e^{-7t}	laplacetransform\:6e^{5t}\cos(2t)-e^{-7t}
integral from 1 to 1000 of 1/(x^3)	\int\:_{1}^{1000}\frac{1}{x^{3}}dx
derivative of (v^3+1)/v	derivative\:\frac{v^{3}+1}{v}
(\partial)/(\partial u)(ln(ucos(v)))	\frac{\partial\:}{\partial\:u}(\ln(u\cos(v)))
laplacetransform f(t)=r^2+6r-3	laplacetransform\:f(t)=r^{2}+6r-3
slope of (3.1)(6.3)	slope\:(3.1)(6.3)
limit as x approaches 3+of (x^2)/(3x-9)	\lim\:_{x\to\:3+}(\frac{x^{2}}{3x-9})
derivative of-2x^4+2x^3-x^2+x	derivative\:-2x^{4}+2x^{3}-x^{2}+x
derivative of y=7e^{sqrt(x)}	derivative\:y=7e^{\sqrt{x}}
tangent of f(x)=\sqrt[4]{4x+2},\at x=1	tangent\:f(x)=\sqrt[4]{4x+2},\at\:x=1
integral of 1/(x^2sqrt(4x^2+49))	\int\:\frac{1}{x^{2}\sqrt{4x^{2}+49}}dx
integral of (-x^2-1)/(x^2-1)	\int\:\frac{-x^{2}-1}{x^{2}-1}dx
derivative of 9e^x(cos(x)-sin(x))	derivative\:9e^{x}(\cos(x)-\sin(x))
sum from n=0 to infinity of (-x)^n	\sum\:_{n=0}^{\infty\:}(-x)^{n}
limit as x approaches 0+of x/(ln(1/x))	\lim\:_{x\to\:0+}(\frac{x}{\ln(\frac{1}{x})})
(\partial)/(\partial x)(y/(2sqrt(x)))	\frac{\partial\:}{\partial\:x}(\frac{y}{2\sqrt{x}})
derivative of x*sin(4/x)	derivative\:x\cdot\:\sin(\frac{4}{x})
x^{''}-8x^'+16x=4te^{4t}	x^{\prime\:\prime\:}-8x^{\prime\:}+16x=4te^{4t}
integral of-cos(4x)	\int\:-\cos(4x)dx
derivative of 7^{x+arccos(x})	\frac{d}{dx}(7^{x+\arccos(x)})
y^{''}+4y^'+20y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+20y=0
(\partial)/(\partial x)(0.0099999)	\frac{\partial\:}{\partial\:x}(0.0099999)
integral of sqrt(1+5x^4)(20x^3)	\int\:\sqrt{1+5x^{4}}(20x^{3})dx
sum from n=1 to infinity of n(3/2)^n	\sum\:_{n=1}^{\infty\:}n(\frac{3}{2})^{n}
derivative of ((x^2+1/(x^2-1))^4)	\frac{d}{dx}((\frac{x^{2}+1}{x^{2}-1})^{4})
derivative of y=cos((pit)/2-pi/3)	derivative\:y=\cos(\frac{πt}{2}-\frac{π}{3})
limit as h approaches 0 of (1-cos(7h))/h	\lim\:_{h\to\:0}(\frac{1-\cos(7h)}{h})
tangent of-2x^2+2x	tangent\:-2x^{2}+2x
limit as x approaches 6 of 21x+18	\lim\:_{x\to\:6}(21x+18)
limit as x approaches-infinity of-(x)	\lim\:_{x\to\:-\infty\:}(-(x))
integral from y to x of cos(e^t)	\int\:_{y}^{x}\cos(e^{t})dt
d/(dt)(t+1/t)	\frac{d}{dt}(t+\frac{1}{t})
integral of (2a^2x^2-b^3)^2	\int\:(2a^{2}x^{2}-b^{3})^{2}dx
integral of 6e^{2t}	\int\:6e^{2t}dt
integral of 1/2 sec^2(x)	\int\:\frac{1}{2}\sec^{2}(x)dx
(\partial)/(\partial x)(sqrt(x^2y^3))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}y^{3}})
integral of (4x)/(x^3+x^2-x-1)	\int\:\frac{4x}{x^{3}+x^{2}-x-1}dx
derivative of-cos(sqrt(x))	\frac{d}{dx}(-\cos(\sqrt{x}))
limit as x approaches-1 of-x^2+2x-9	\lim\:_{x\to\:-1}(-x^{2}+2x-9)
-y^'+(4y)/x =xy^2	-y^{\prime\:}+\frac{4y}{x}=xy^{2}
integral of (x^2)/((x^3+1)^5)	\int\:\frac{x^{2}}{(x^{3}+1)^{5}}dx
inverse oflaplace s/(s^2+4s+3)	inverselaplace\:\frac{s}{s^{2}+4s+3}
(\partial)/(\partial x)(4x^{0.75}+y)	\frac{\partial\:}{\partial\:x}(4x^{0.75}+y)
integral of-729cot^3(θ)csc(θ)	\int\:-729\cot^{3}(θ)\csc(θ)dθ
integral of sqrt(1-x^2-y^2)	\int\:\sqrt{1-x^{2}-y^{2}}dy
integral of 1/(sqrt(t^2-8t+41))	\int\:\frac{1}{\sqrt{t^{2}-8t+41}}dt
derivative of 8x(x^5+1^3)	\frac{d}{dx}(8x(x^{5}+1)^{3})
(\partial)/(\partial x)(4+x+x^2y)	\frac{\partial\:}{\partial\:x}(4+x+x^{2}y)
limit as x approaches 0 of 4/x	\lim\:_{x\to\:0}(\frac{4}{x})
derivative of 2x^2-6	\frac{d}{dx}(2x^{2}-6)
laplacetransform e^{-3s}	laplacetransform\:e^{-3s}
(\partial)/(\partial y)(3y^2+10xy^2)	\frac{\partial\:}{\partial\:y}(3y^{2}+10xy^{2})
integral of 1/((x+1)^2(x-5))	\int\:\frac{1}{(x+1)^{2}(x-5)}dx
derivative of xsin(2/x)	\frac{d}{dx}(x\sin(\frac{2}{x}))
(\partial)/(\partial x)((-y)/(2x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{-y}{2x^{2}+y^{2}})
derivative of (x^2-2x)(2x-x^2)	derivative\:(x^{2}-2x)(2x-x^{2})
(\partial)/(\partial t)(te^{st})	\frac{\partial\:}{\partial\:t}(te^{st})
derivative of (x-1tan(x)+xsin(pix))	\frac{d}{dx}((x-1)\tan(x)+x\sin(πx))
(2xy)dx+(x^2-1)dy=0	(2xy)dx+(x^{2}-1)dy=0
derivative of 8/(x^6)	derivative\:\frac{8}{x^{6}}
derivative of 3/((x^2-5x^2))	\frac{d}{dx}(\frac{3}{(x^{2}-5x)^{2}})
integral of (1-y)/y	\int\:\frac{1-y}{y}dy
integral from 0 to 2.1 of pi(21/10-x)^2	\int\:_{0}^{2.1}π(\frac{21}{10}-x)^{2}dx
(\partial ^2)/(\partial y^2)(ln(2+x^2y^2))	\frac{\partial\:^{2}}{\partial\:y^{2}}(\ln(2+x^{2}y^{2}))
integral of tan^3(x)sec^6(x)	\int\:\tan^{3}(x)\sec^{6}(x)dx
integral of 1/9 x^{-2/9}	\int\:\frac{1}{9}x^{-\frac{2}{9}}dx
(\partial)/(\partial x)(y^2*x)	\frac{\partial\:}{\partial\:x}(y^{2}\cdot\:x)
integral from 1 to 9 of 1/(2x^2)	\int\:_{1}^{9}\frac{1}{2x^{2}}dx
x^2y^{''}+2xy^'-12y=0,y(1)=-1,y^'(1)=10	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-12y=0,y(1)=-1,y^{\prime\:}(1)=10
(dx)/(dy)=-(4y^2+6xy)/(3y^2+2x)	\frac{dx}{dy}=-\frac{4y^{2}+6xy}{3y^{2}+2x}
limit as x approaches 2 of x^4	\lim\:_{x\to\:2}(x^{4})
derivative of f(x)= 2/(x-3)	derivative\:f(x)=\frac{2}{x-3}
slope of y=sqrt(1-x^2),\at x= 1/2	slope\:y=\sqrt{1-x^{2}},\at\:x=\frac{1}{2}
limit as x approaches 9 of ((16+sqrt(x)))/(sqrt(16+x))	\lim\:_{x\to\:9}(\frac{(16+\sqrt{x})}{\sqrt{16+x}})
maclaurin f(x)=e^{x/2}	maclaurin\:f(x)=e^{\frac{x}{2}}
inverse oflaplace {((s+1)^2)/(s^3)}	inverselaplace\:\left\{\frac{(s+1)^{2}}{s^{3}}\right\}
y^'=(xy^3)/(25)	y^{\prime\:}=\frac{xy^{3}}{25}
(\partial)/(\partial y)(sqrt(1-y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{1-y^{2}})
derivative of 2sin(x)	derivative\:2\sin(x)

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