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Popular Calculus Problems

limit as x approaches 0 of 1/(x^2(x+7))	\lim\:_{x\to\:0}(\frac{1}{x^{2}(x+7)})
laplacetransform t*cos(kt)	laplacetransform\:t\cdot\:\cos(kt)
integral of 1/(9x-4)	\int\:\frac{1}{9x-4}dx
integral of (x^2-2x)/(x^3-3x^2+1)	\int\:\frac{x^{2}-2x}{x^{3}-3x^{2}+1}dx
derivative of e^{sin(x}*cos(sin(x)))	\frac{d}{dx}(e^{\sin(x)}\cdot\:\cos(\sin(x)))
y^'-8/x y=(y^4)/(x^{18)}	y^{\prime\:}-\frac{8}{x}y=\frac{y^{4}}{x^{18}}
integral of X^2	\int\:X^{2}dX
(\partial)/(\partial x)(2y^3+4x)	\frac{\partial\:}{\partial\:x}(2y^{3}+4x)
integral of (2-8x)/(sqrt(9-4x^2))	\int\:\frac{2-8x}{\sqrt{9-4x^{2}}}dx
tangent of y=2x^2-9x+7	tangent\:y=2x^{2}-9x+7
derivative of 1/(2cos^2(x))	\frac{d}{dx}(\frac{1}{2\cos^{2}(x)})
integral of (xsqrt(x+2))	\int\:(x\sqrt{x+2})dx
tangent of y=9+4x^2-2x^3,(1,11)	tangent\:y=9+4x^{2}-2x^{3},(1,11)
derivative of 9/(ln(x))	\frac{d}{dx}(\frac{9}{\ln(x)})
integral of-4t	\int\:-4tdt
derivative of f(x)=-sqrt(1-x)x^2	derivative\:f(x)=-\sqrt{1-x}x^{2}
integral of cos(22x)cos(17x)	\int\:\cos(22x)\cos(17x)dx
sum from n=3 to infinity of 5^n	\sum\:_{n=3}^{\infty\:}5^{n}
(y^2+1)dx=(ysec^2(x))dy	(y^{2}+1)dx=(y\sec^{2}(x))dy
((2t+1)/(2t))^'	(\frac{2t+1}{2t})^{\prime\:}
(\partial)/(\partial r)(arctan(rs))	\frac{\partial\:}{\partial\:r}(\arctan(rs))
(d^5)/(dx^5)(ln(x+1))	\frac{d^{5}}{dx^{5}}(\ln(x+1))
(\partial)/(\partial x)(sqrt(4+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{4+x^{2}+y^{2}})
integral of 21tan^3(x)	\int\:21\tan^{3}(x)dx
derivative of 6(x^3-3(x)(y)+3(y)^3)	\frac{d}{dx}(6(x)^{3}-3(x)(y)+3(y)^{3})
integral from 0 to 5 of 6/(7x^2+8x+1)	\int\:_{0}^{5}\frac{6}{7x^{2}+8x+1}dx
integral of x^2(4x^3+2)^3	\int\:x^{2}(4x^{3}+2)^{3}dx
tangent of y=x^2,(-1,-3)	tangent\:y=x^{2},(-1,-3)
integral from v^1 to v^2 of 1/v	\int\:_{v^{1}}^{v^{2}}\frac{1}{v}dv
limit as x approaches-1 of 1/(x^2-1)	\lim\:_{x\to\:-1}(\frac{1}{x^{2}-1})
(d^2)/(dx^2)(9xsin(x^2))	\frac{d^{2}}{dx^{2}}(9x\sin(x^{2}))
(\partial)/(\partial x)(2x+1)	\frac{\partial\:}{\partial\:x}(2x+1)
(\partial)/(\partial z)(zcos(xz))	\frac{\partial\:}{\partial\:z}(z\cos(xz))
integral from 1 to 2 of 2r^2ln(r)	\int\:_{1}^{2}2r^{2}\ln(r)dr
integral of 0.75e	\int\:0.75edk
integral of sqrt(1/x-1) 1/(x^2)	\int\:\sqrt{\frac{1}{x}-1}\frac{1}{x^{2}}dx
inverse oflaplace 4/(s(s^2+s))	inverselaplace\:\frac{4}{s(s^{2}+s)}
integral of 2x-6y	\int\:2x-6ydx
(\partial)/(\partial x)(x^4y-2x^3y^2)	\frac{\partial\:}{\partial\:x}(x^{4}y-2x^{3}y^{2})
integral of e x/2	\int\:e\frac{x}{2}dx
limit as x approaches 3+of (3-x)/(\|x-3\|)	\lim\:_{x\to\:3+}(\frac{3-x}{\left\|x-3\right\|})
y^'=ln(x)	y^{\prime\:}=\ln(x)
laplacetransform f(t)=(1+e^{4t})^2	laplacetransform\:f(t)=(1+e^{4t})^{2}
integral of (3x+1)/(x(x+1)^2)	\int\:\frac{3x+1}{x(x+1)^{2}}dx
laplacetransform e^{-2t-5}	laplacetransform\:e^{-2t-5}
(\partial)/(\partial x)(y*ln(x))	\frac{\partial\:}{\partial\:x}(y\cdot\:\ln(x))
integral of (x+1)/(x^3-x^2)	\int\:\frac{x+1}{x^{3}-x^{2}}dx
integral from 0 to pi of sin^2(x)	\int\:_{0}^{π}\sin^{2}(x)dx
(\partial)/(\partial x)(ln(4-x^2))	\frac{\partial\:}{\partial\:x}(\ln(4-x^{2}))
tangent of y=4x^2-x^3,(1,3)	tangent\:y=4x^{2}-x^{3},(1,3)
slope ofintercept (0.1)(1.1)	slopeintercept\:(0.1)(1.1)
limit as x approaches a of sqrt(0)	\lim\:_{x\to\:a}(\sqrt{0})
derivative of f(x)=xsqrt(x+3)	derivative\:f(x)=x\sqrt{x+3}
integral of (5x)/x	\int\:\frac{5x}{x}dx
integral of 5sec^5(x)	\int\:5\sec^{5}(x)dx
integral of-e^{-t}+1	\int\:-e^{-t}+1dt
tangent of f(x)=x^4-10x^2+9,\at x=1	tangent\:f(x)=x^{4}-10x^{2}+9,\at\:x=1
derivative of h(g(x)k(x))	derivative\:h(g(x)k(x))
derivative of 2/3 (1+x)^{3/2}	derivative\:\frac{2}{3}(1+x)^{\frac{3}{2}}
tangent of f(x)=3e^x,\at x=0	tangent\:f(x)=3e^{x},\at\:x=0
y^'=-5y+5t^2+2t,y(0)= 1/3	y^{\prime\:}=-5y+5t^{2}+2t,y(0)=\frac{1}{3}
integral of 3/(sqrt(4-x^2))	\int\:\frac{3}{\sqrt{4-x^{2}}}dx
d/(dθ)(θ-sin(θ))	\frac{d}{dθ}(θ-\sin(θ))
limit as x approaches 0 of 1/(sin(x))	\lim\:_{x\to\:0}(\frac{1}{\sin(x)})
(\partial)/(\partial x)(y/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{(x+y)^{2}})
derivative of 6x^2-x^3	\frac{d}{dx}(6x^{2}-x^{3})
derivative of 7x^2-x^3	derivative\:7x^{2}-x^{3}
(\partial)/(\partial y)(x^2e^{-y})	\frac{\partial\:}{\partial\:y}(x^{2}e^{-y})
limit as x approaches 0 of (1-x)^{1/x}	\lim\:_{x\to\:0}((1-x)^{\frac{1}{x}})
d/(dt)(-st)	\frac{d}{dt}(-st)
derivative of (u^{-2}+u^{-3})(u^5-4u^2)	derivative\:(u^{-2}+u^{-3})(u^{5}-4u^{2})
y^'=((y+3)/(4x+5))^3	y^{\prime\:}=(\frac{y+3}{4x+5})^{3}
integral of y(y^2+1)^5	\int\:y(y^{2}+1)^{5}dy
limit as x approaches-6 of ((x+7))/(x+6)	\lim\:_{x\to\:-6}(\frac{(x+7)}{x+6})
integral of (6e^{2x})/(e^{2x)+12e^x+27}	\int\:\frac{6e^{2x}}{e^{2x}+12e^{x}+27}dx
integral of sqrt(x)(x^2+sqrt(x))	\int\:\sqrt{x}(x^{2}+\sqrt{x})dx
integral of x(a-bx^2)	\int\:x(a-bx^{2})dx
tangent of f(x)=2x^2+x-2,\at x=4	tangent\:f(x)=2x^{2}+x-2,\at\:x=4
integral of (-1600x)/(sqrt(25-x^2))	\int\:\frac{-1600x}{\sqrt{25-x^{2}}}dx
integral of 1/(xsqrt(8x+81))	\int\:\frac{1}{x\sqrt{8x+81}}dx
(\partial)/(\partial x)(x+e^y)	\frac{\partial\:}{\partial\:x}(x+e^{y})
(\partial)/(\partial x)(4x+8y-88)	\frac{\partial\:}{\partial\:x}(4x+8y-88)
derivative of f(x)=-x^{2/3}(x-5)	derivative\:f(x)=-x^{\frac{2}{3}}(x-5)
integral of 3(1-x)^2	\int\:3(1-x)^{2}dx
integral of x^{1/2}+6	\int\:x^{\frac{1}{2}}+6dx
integral from 0 to 2 of x^3(2-x)^2	\int\:_{0}^{2}x^{3}(2-x)^{2}dx
limit as x approaches 0 of (e^x)/(ln(x))	\lim\:_{x\to\:0}(\frac{e^{x}}{\ln(x)})
derivative of (3x^2+x)/(-x^2+3x-3)	derivative\:\frac{3x^{2}+x}{-x^{2}+3x-3}
tangent of 17-x^2	tangent\:17-x^{2}
derivative of xe^xcsc(x)	derivative\:xe^{x}\csc(x)
integral of 6y^2+1/(24y^2)	\int\:6y^{2}+\frac{1}{24y^{2}}dy
derivative of-5pisin(10pix)	derivative\:-5π\sin(10πx)
(\partial)/(\partial y)(4x^3y)	\frac{\partial\:}{\partial\:y}(4x^{3}y)
limit as x approaches 0+of (7e^x)/(x^5)	\lim\:_{x\to\:0+}(\frac{7e^{x}}{x^{5}})
limit as x approaches 0 of (e^0-1)/x	\lim\:_{x\to\:0}(\frac{e^{0}-1}{x})
integral from 1 to e of ln(x)	\int\:_{1}^{e}\ln(x)dx
integral of 3/(100+2t)	\int\:\frac{3}{100+2t}dt
integral from 0 to 1 of 18 1/(x^p)	\int\:_{0}^{1}18\frac{1}{x^{p}}dx
tangent of y=x(1-2x)^3,(1,-1)	tangent\:y=x(1-2x)^{3},(1,-1)
(\partial)/(\partial y)(x^3ln(y^6))	\frac{\partial\:}{\partial\:y}(x^{3}\ln(y^{6}))

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