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Popular Calculus Problems

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}
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)
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))
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
(\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}
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})
laplacetransform e^{-3s}	laplacetransform\:e^{-3s}
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 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))
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
(\partial ^2)/(\partial y^2)(ln(2+x^2y^2))	\frac{\partial\:^{2}}{\partial\:y^{2}}(\ln(2+x^{2}y^{2}))
integral of 1/9 x^{-2/9}	\int\:\frac{1}{9}x^{-\frac{2}{9}}dx
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)
integral of (2x+1)/(e^{2x)}	\int\:\frac{2x+1}{e^{2x}}dx
(\partial)/(\partial x)(e^xcos(y)+2x-3y^2)	\frac{\partial\:}{\partial\:x}(e^{x}\cos(y)+2x-3y^{2})
taylor 2+t+1/t	taylor\:2+t+\frac{1}{t}
integral of (x+1)/(x(x-1)^2)	\int\:\frac{x+1}{x(x-1)^{2}}dx
derivative of 5cos(5x)	\frac{d}{dx}(5\cos(5x))
derivative of (x(x+1)/(2x-1))	\frac{d}{dx}(\frac{x(x+1)}{2x-1})
integral of 1/(x(sqrt(x)+1))	\int\:\frac{1}{x(\sqrt{x}+1)}dx
derivative of y=2-x^2	derivative\:y=2-x^{2}
integral from-2pi to pi of pisin^2(x)	\int\:_{-2π}^{π}π\sin^{2}(x)dx
(dy}{dx}=\frac{x^2-x+2)/x+y	\frac{dy}{dx}=\frac{x^{2}-x+2}{x}+y
integral of 5sin(5x-3)	\int\:5\sin(5x-3)dx
derivative of \sqrt[4]{x}-4e^x	derivative\:\sqrt[4]{x}-4e^{x}
area sin(x),5-x^2,[-2.384677,2.0252116]	area\:\sin(x),5-x^{2},[-2.384677,2.0252116]
integral of (2x)/(a^2)	\int\:\frac{2x}{a^{2}}dx
integral of (x^e+e^x+x+e)	\int\:(x^{e}+e^{x}+x+e)dx
integral of sin(x)-xcos(x)	\int\:\sin(x)-x\cos(x)dx
integral of 1+ye^{(xy)}	\int\:1+ye^{(xy)}dx
integral of usqrt(u+4)	\int\:u\sqrt{u+4}du
derivative of 1/((3+t)^2)	derivative\:\frac{1}{(3+t)^{2}}
(\partial)/(\partial y)(xln(x^2+y^2))	\frac{\partial\:}{\partial\:y}(x\ln(x^{2}+y^{2}))
integral from-1 to 4 of \|x-3x^2\|	\int\:_{-1}^{4}\left\|x-3x^{2}\right\|dx
(xe^{x^2})^'	(xe^{x^{2}})^{\prime\:}
(\partial)/(\partial x)(e^{xy-y})	\frac{\partial\:}{\partial\:x}(e^{xy-y})
derivative of e^{3xcos(2x)}	derivative\:e^{3x\cos(2x)}
derivative of y=-3/x+2/(x^3)	derivative\:y=-\frac{3}{x}+\frac{2}{x^{3}}
integral of (7-x^2)/(3x^3+x)	\int\:\frac{7-x^{2}}{3x^{3}+x}dx
tangent of f(x)=x^2+x,\at a=5	tangent\:f(x)=x^{2}+x,\at\:a=5
integral of (13)/(x(x^2+4)^2)	\int\:\frac{13}{x(x^{2}+4)^{2}}dx
integral of (16)/((t^2+1)^{3/2)}	\int\:\frac{16}{(t^{2}+1)^{\frac{3}{2}}}dt
derivative of-4x+1/x-3	derivative\:-4x+\frac{1}{x}-3
(\partial)/(\partial x)(x^2+2y+2z-12)	\frac{\partial\:}{\partial\:x}(x^{2}+2y+2z-12)

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