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Popular Calculus Problems

integral of (csc^2(x)-2e^x)	\int\:(\csc^{2}(x)-2e^{x})dx
limit as x approaches 2 of x^3+4x^2-2x+2	\lim\:_{x\to\:2}(x^{3}+4x^{2}-2x+2)
derivative of f(x)=2x^2e^x(x^2-3x+1)	derivative\:f(x)=2x^{2}e^{x}(x^{2}-3x+1)
integral of 2x*e^x	\int\:2x\cdot\:e^{x}dx
integral of t^8	\int\:t^{8}dt
integral from 1 to 4 of (x-7)/(sqrt(x))	\int\:_{1}^{4}\frac{x-7}{\sqrt{x}}dx
(\partial)/(\partial x)(2(1-e^x)^2)	\frac{\partial\:}{\partial\:x}(2(1-e^{x})^{2})
derivative of (3x^3+4)^2	derivative\:(3x^{3}+4)^{2}
integral of (x^{-4}+1/(sqrt(x)))	\int\:(x^{-4}+\frac{1}{\sqrt{x}})dx
derivative of (11x^4+5^3)	\frac{d}{dx}((11x^{4}+5)^{3})
integral of ((ln(x^3))/x)	\int\:(\frac{\ln(x^{3})}{x})dx
integral from 0 to 4 of (x^2+1)	\int\:_{0}^{4}(x^{2}+1)dx
integral of xsec^2(9x)	\int\:x\sec^{2}(9x)dx
y^'-9/x y=(y^4)/(x^{12)},y(1)=1	y^{\prime\:}-\frac{9}{x}y=\frac{y^{4}}{x^{12}},y(1)=1
(\partial)/(\partial y)(xcos(x+y))	\frac{\partial\:}{\partial\:y}(x\cos(x+y))
(dy)/(dx)+2y=20e^{3x}	\frac{dy}{dx}+2y=20e^{3x}
(\partial)/(\partial y)((7y)/(x^4))	\frac{\partial\:}{\partial\:y}(\frac{7y}{x^{4}})
limit as x approaches 1 of 2x-5	\lim\:_{x\to\:1}(2x-5)
derivative of 1/8 x^2	\frac{d}{dx}(\frac{1}{8}x^{2})
integral from 0 to 1 of (1-x)^2	\int\:_{0}^{1}(1-x)^{2}dx
(\partial)/(\partial x)(-y^2sin(xy^2))	\frac{\partial\:}{\partial\:x}(-y^{2}\sin(xy^{2}))
derivative of (x-1^4)	\frac{d}{dx}((x-1)^{4})
integral of sin^3(θ)cos^8(θ)	\int\:\sin^{3}(θ)\cos^{8}(θ)dθ
integral of 3/(3sin(x)-4cos(x))	\int\:\frac{3}{3\sin(x)-4\cos(x)}dx
derivative of 1/(cot(1/t))	derivative\:\frac{1}{\cot(\frac{1}{t})}
derivative of 3^{cos(2x})	\frac{d}{dx}(3^{\cos(2x)})
limit as x approaches 3 of (10)/(x^2)	\lim\:_{x\to\:3}(\frac{10}{x^{2}})
integral from 0 to 4 of ((5x)/(x^2+9))	\int\:_{0}^{4}(\frac{5x}{x^{2}+9})dx
integral of (x+6)(x-7)	\int\:(x+6)(x-7)dx
(\partial)/(\partial x)((x+q)/(x+r))	\frac{\partial\:}{\partial\:x}(\frac{x+q}{x+r})
derivative of (2x+sqrt(x)(x^2-x))	\frac{d}{dx}((2x+\sqrt{x})(x^{2}-x))
derivative of sec^2(θ)	derivative\:\sec^{2}(θ)
derivative of (cos(x)/(x^6))	\frac{d}{dx}(\frac{\cos(x)}{x^{6}})
taylor 1/(2-x)	taylor\:\frac{1}{2-x}
integral of (1+x+e^x)	\int\:(1+x+e^{x})dx
f(z)=tan(e^{-6z})	f(z)=\tan(e^{-6z})
derivative of sin^4(2x+3)	\frac{d}{dx}(\sin^{4}(2x+3))
derivative of (1/x)^3	derivative\:(\frac{1}{x})^{3}
tangent of f(x)=(3x-1)/(x^2+1),\at x=6	tangent\:f(x)=\frac{3x-1}{x^{2}+1},\at\:x=6
integral from 1 to 2 of (4x^2-7x-12)/(x(x+2)(x-3))	\int\:_{1}^{2}\frac{4x^{2}-7x-12}{x(x+2)(x-3)}dx
derivative of x^{-3/5}	\frac{d}{dx}(x^{-\frac{3}{5}})
derivative of y=ln(x^2+5)	derivative\:y=\ln(x^{2}+5)
integral of 1/(xsqrt(x^2-16))	\int\:\frac{1}{x\sqrt{x^{2}-16}}dx
(dy)/(dx)=(x-y^2)/(2xy+y)	\frac{dy}{dx}=\frac{x-y^{2}}{2xy+y}
integral of (sin(2x)+cos(2x))	\int\:(\sin(2x)+\cos(2x))dx
area y=x^2,y=2x-x^2	area\:y=x^{2},y=2x-x^{2}
derivative of (qx+r(q,x,t)/(sx+t))	\frac{d}{dx}(\frac{qx+r(q,x,t)}{sx+t})
integral of (x+4)sqrt(6-x)	\int\:(x+4)\sqrt{6-x}dx
integral of (2x^3)/(sqrt(x^2-4))	\int\:\frac{2x^{3}}{\sqrt{x^{2}-4}}dx
derivative of 3x^3+2x+9	\frac{d}{dx}(3x^{3}+2x+9)
limit as x approaches 0+of (csc(x))^x	\lim\:_{x\to\:0+}((\csc(x))^{x})
(\partial)/(\partial x)(xsin(y)sin(z))	\frac{\partial\:}{\partial\:x}(x\cdot\:\sin(y)\cdot\:\sin(z))
derivative of x^2+6x+3	derivative\:x^{2}+6x+3
derivative of \sqrt[3]{(1+x^3/(1-x^3)})	\frac{d}{dx}(\sqrt[3]{\frac{1+x^{3}}{1-x^{3}}})
limit as x approaches 8+of ln(x^2-64)	\lim\:_{x\to\:8+}(\ln(x^{2}-64))
(\partial)/(\partial x)(x+1/2 y)	\frac{\partial\:}{\partial\:x}(x+\frac{1}{2}y)
taylor 1/(1-x),1.1	taylor\:\frac{1}{1-x},1.1
implicit (dy)/(dx),y=1.1x+0.077x^2	implicit\:\frac{dy}{dx},y=1.1x+0.077x^{2}
inverse oflaplace 3/((s+2)*(4s^2+4s+5))	inverselaplace\:\frac{3}{(s+2)\cdot\:(4s^{2}+4s+5)}
derivative of x^4-3x^3+2x^2	\frac{d}{dx}(x^{4}-3x^{3}+2x^{2})
limit as x approaches 4 of (8x-4)/(x+6)	\lim\:_{x\to\:4}(\frac{8x-4}{x+6})
(log_{10}(x+1))^'	(\log_{10}(x+1))^{\prime\:}
limit as x approaches infinity of (3x+5)/(6x-8)	\lim\:_{x\to\:\infty\:}(\frac{3x+5}{6x-8})
derivative of sin^{2/3}(x)	\frac{d}{dx}(\sin^{\frac{2}{3}}(x))
derivative of 4sin(x+4xcos(x))	\frac{d}{dx}(4\sin(x)+4x\cos(x))
sum from n=0 to infinity of (4/7)^n	\sum\:_{n=0}^{\infty\:}(\frac{4}{7})^{n}
(dy)/(dx)=(((1+y)^2))/((1+x)^3),y(1)=0	\frac{dy}{dx}=\frac{((1+y)^{2})}{(1+x)^{3}},y(1)=0
(\partial)/(\partial x)(ln(x+5y+8z))	\frac{\partial\:}{\partial\:x}(\ln(x+5y+8z))
limit as t approaches-3 of e^t	\lim\:_{t\to\:-3}(e^{t})
(\partial)/(\partial y)(x/(x^4-y^3))	\frac{\partial\:}{\partial\:y}(\frac{x}{x^{4}-y^{3}})
limit as x approaches-1 of 2x^3+x+7	\lim\:_{x\to\:-1}(2x^{3}+x+7)
limit as x approaches 1+of 2x+4	\lim\:_{x\to\:1+}(2x+4)
inverse oflaplace {(10s)/(s^2+16)}	inverselaplace\:\left\{\frac{10s}{s^{2}+16}\right\}
integral from-2 to 2 of 1/((x+1)^4)	\int\:_{-2}^{2}\frac{1}{(x+1)^{4}}dx
derivative of (4x/5)	\frac{d}{dx}(\frac{4x}{5})
f^'(x)=12x^3-63x^2-72x+4	f^{\prime\:}(x)=12x^{3}-63x^{2}-72x+4
derivative of y=(f(x))/(x^6)	derivative\:y=\frac{f(x)}{x^{6}}
derivative of y=acsc(2)(kx)	derivative\:y=a\csc(2)(kx)
integral from 0 to 1 of x-x^k	\int\:_{0}^{1}x-x^{k}dx
derivative of 3x+y	\frac{d}{dx}(3x+y)
derivative of 3	derivative\:3
integral of (3x+5)	\int\:(3x+5)dx
derivative of arctan(x/(2000))	\frac{d}{dx}(\arctan(\frac{x}{2000}))
(1/((1+x)^2))^'	(\frac{1}{(1+x)^{2}})^{\prime\:}
integral of sqrt(x)*(e^{sqrt(x)})/(2x)	\int\:\sqrt{x}\cdot\:\frac{e^{\sqrt{x}}}{2x}dx
derivative of xe^{3{z}(x})	\frac{d}{dx}(xe^{3{z}(x)})
tangent of f(x)=x^3+2/x ,\at x=1	tangent\:f(x)=x^{3}+\frac{2}{x},\at\:x=1
laplacetransform \delta(t)	laplacetransform\:\delta(t)
y^'-2y=5	y^{\prime\:}-2y=5
integral of (ln(sqrt(6x)))/x	\int\:\frac{\ln(\sqrt{6x})}{x}dx
integral from 6 to 9 of (x-7)^2	\int\:_{6}^{9}(x-7)^{2}dx
integral of cos(x)(7+5sin^2(x))	\int\:\cos(x)(7+5\sin^{2}(x))dx
derivative of 5x^7	\frac{d}{dx}(5x^{7})
integral from 0 to pi of cos(x)sin(nx)	\int\:_{0}^{π}\cos(x)\sin(nx)dx
limit as x approaches 3 of x^2+1	\lim\:_{x\to\:3}(x^{2}+1)
integral of-t/2	\int\:-\frac{t}{2}dt
(dy)/(dx)=6+sqrt(y-6x+4)	\frac{dy}{dx}=6+\sqrt{y-6x+4}
integral from 0 to 4 of-x^2+4x	\int\:_{0}^{4}-x^{2}+4xdx
derivative of arccos(5x^8)	derivative\:\arccos(5x^{8})
derivative of (7x^2-1/x)	\frac{d}{dx}(\frac{7x^{2}-1}{x})

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