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Popular Calculus Problems

integral of 1/(25x^2-4)	\int\:\frac{1}{25x^{2}-4}dx
derivative of 1/2 x^3+1/(6x)	\frac{d}{dx}(\frac{1}{2}x^{3}+\frac{1}{6x})
(\partial)/(\partial x)(3^4-65^3)	\frac{\partial\:}{\partial\:x}(3^{4}-65^{3})
y^'=3y-2x	y^{\prime\:}=3y-2x
area 5cos(7x),5-5cos(7x),[0, pi/7 ]	area\:5\cos(7x),5-5\cos(7x),[0,\frac{π}{7}]
y^'+y/(6.96)=0.0025862069	y^{\prime\:}+\frac{y}{6.96}=0.0025862069
derivative of ln(x^{1/5})	\frac{d}{dx}(\ln(x^{\frac{1}{5}}))
integral of x^2+x^{-2}	\int\:x^{2}+x^{-2}dx
sin(2x)dx+cos(6y)dy=0	\sin(2x)dx+\cos(6y)dy=0
integral of x/(\sqrt[5]{x^2-1)}	\int\:\frac{x}{\sqrt[5]{x^{2}-1}}dx
derivative of (2x-3)^2	derivative\:(2x-3)^{2}
(\partial)/(\partial x)(xe^{-x}(Ax^2+Bx+C))	\frac{\partial\:}{\partial\:x}(xe^{-x}(Ax^{2}+Bx+C))
integral of-(ln(x))/x	\int\:-\frac{\ln(x)}{x}dx
(dy)/(y-y^2)=dx	\frac{dy}{y-y^{2}}=dx
integral of 3/5 x^{1/3}	\int\:\frac{3}{5}x^{\frac{1}{3}}dx
derivative of (ax+be^x)	\frac{d}{dx}((ax+b)e^{x})
tangent of f(x)=sqrt(x^2-x+10),\at x=3	tangent\:f(x)=\sqrt{x^{2}-x+10},\at\:x=3
integral of 1/(v*sqrt(v^2-1))	\int\:\frac{1}{v\cdot\:\sqrt{v^{2}-1}}dv
integral of cot(3x)	\int\:\cot(3x)dx
simplify ln(xsqrt(x^2-5))	simplify\:\ln(x\sqrt{x^{2}-5})
taylor 7/(1-x)	taylor\:\frac{7}{1-x}
derivative of x^2+x+8	derivative\:x^{2}+x+8
derivative of f(x)=ln(e^x)	derivative\:f(x)=\ln(e^{x})
integral of (e^{-2x})	\int\:(e^{-2x})dx
integral of 6(2x-3)^{-6}	\int\:6(2x-3)^{-6}dx
integral of 1/(x^2+6x+13)	\int\:\frac{1}{x^{2}+6x+13}dx
integral of (1/(sqrt(x)))	\int\:(\frac{1}{\sqrt{x}})dx
derivative of e^{-x}*sin(x)	\frac{d}{dx}(e^{-x}\cdot\:\sin(x))
derivative of e^{1/(x^3})	\frac{d}{dx}(e^{\frac{1}{x^{3}}})
(dy)/(dx)y=(y+1)(2x+1),y(-1)=1	\frac{dy}{dx}y=(y+1)(2x+1),y(-1)=1
integral of z^2(z^3-1)^6	\int\:z^{2}(z^{3}-1)^{6}dz
integral of p(p+6)^5	\int\:p(p+6)^{5}dp
integral of 2/(1-4x^2)	\int\:\frac{2}{1-4x^{2}}dx
tangent of f(x)=2x-x^2,\at x=1	tangent\:f(x)=2x-x^{2},\at\:x=1
derivative of (x^3-1/(ln(x)))	\frac{d}{dx}(\frac{x^{3}-1}{\ln(x)})
integral of cos(x)sin(x)sqrt(1+cos^2(x))	\int\:\cos(x)\sin(x)\sqrt{1+\cos^{2}(x)}dx
4y^{''}-16y=0	4y^{\prime\:\prime\:}-16y=0
integral of 4tan(x)	\int\:4\tan(x)dx
derivative of f(x)=2e^x	derivative\:f(x)=2e^{x}
(ln(3x+1))^'	(\ln(3x+1))^{\prime\:}
laplacetransform (cos(4t)-8)^2	laplacetransform\:(\cos(4t)-8)^{2}
(dy)/(dx)+6tan(6x)y=-8cos(6x)	\frac{dy}{dx}+6\tan(6x)y=-8\cos(6x)
integral of (x-1)/(x^2+2x)	\int\:\frac{x-1}{x^{2}+2x}dx
taylor sqrt((1-x^2))	taylor\:\sqrt{(1-x^{2})}
integral of 8(tan^3(2sqrt(x)))/(sqrt(x))	\int\:8\frac{\tan^{3}(2\sqrt{x})}{\sqrt{x}}dx
sum from n=2 to infinity of n(n-1)x^n	\sum\:_{n=2}^{\infty\:}n(n-1)x^{n}
limit as x approaches-2 of (x^2-3)/(x+1)	\lim\:_{x\to\:-2}(\frac{x^{2}-3}{x+1})
derivative of f(x)=(9x^6+2x^3)^4	derivative\:f(x)=(9x^{6}+2x^{3})^{4}
integral of (sec(x))/(sin(x))	\int\:\frac{\sec(x)}{\sin(x)}dx
derivative of (sin(3x)^3)	\frac{d}{dx}((\sin(3x))^{3})
(\partial)/(\partial x)(-5xcos(x^2-5xy))	\frac{\partial\:}{\partial\:x}(-5x\cos(x^{2}-5xy))
(d^2)/(dx)(y)+2(dy)/(dx)+y=0	\frac{d^{2}}{dx}(y)+2\frac{dy}{dx}+y=0
(\partial)/(\partial x)(e^{-2z}ysin(x))	\frac{\partial\:}{\partial\:x}(e^{-2z}y\sin(x))
area cos(θ),0.5	area\:\cos(θ),0.5
derivative of 153x^2-0.06x^3	derivative\:153x^{2}-0.06x^{3}
derivative of y=(3/5 x)^4	derivative\:y=(\frac{3}{5}x)^{4}
derivative of f(x)=ln(7x)	derivative\:f(x)=\ln(7x)
(\partial)/(\partial z)(y/(1+x^2y^2))	\frac{\partial\:}{\partial\:z}(\frac{y}{1+x^{2}y^{2}})
derivative of x^9sin(x)	derivative\:x^{9}\sin(x)
derivative of (x-5)(5x+3)	derivative\:(x-5)(5x+3)
derivative of x^{-4}	derivative\:x^{-4}
integral from 2 to 4 of 6/(2x-9)	\int\:_{2}^{4}\frac{6}{2x-9}dx
limit as x approaches 8 of x+2	\lim\:_{x\to\:8}(x+2)
tangent of f(x)=ln(x^3-7),\at x=2	tangent\:f(x)=\ln(x^{3}-7),\at\:x=2
integral of 1/(xsqrt(x)+x^2)	\int\:\frac{1}{x\sqrt{x}+x^{2}}dx
integral from 0 to L of sin^2((npix)/L)	\int\:_{0}^{L}\sin^{2}(\frac{nπx}{L})dx
derivative of y=(e^x)/(1+x)	derivative\:y=\frac{e^{x}}{1+x}
derivative of tan^2(6x)	derivative\:\tan^{2}(6x)
integral from 1 to 3 of (x^2+3)/(4x-x^2)	\int\:_{1}^{3}\frac{x^{2}+3}{4x-x^{2}}dx
(\partial)/(\partial y)(sqrt(38-x^2-4y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{38-x^{2}-4y^{2}})
x^4+y^3sqrt(x^5+4)(dy)/(dx)=0,y(1)=0	x^{4}+y^{3}\sqrt{x^{5}+4}\frac{dy}{dx}=0,y(1)=0
derivative of e^{ktan(sqrt(3x)})	\frac{d}{dx}(e^{k\tan(\sqrt{3x})})
integral of-64x^3sin(4x^4+3)	\int\:-64x^{3}\sin(4x^{4}+3)dx
limit as h approaches 0 of ((1+h)^7-1)/h	\lim\:_{h\to\:0}(\frac{(1+h)^{7}-1}{h})
derivative of f(x)= 4/3 x-7	derivative\:f(x)=\frac{4}{3}x-7
(\partial)/(\partial x)((1-x)^2)	\frac{\partial\:}{\partial\:x}((1-x)^{2})
d/(dt)((ce^t)/(1+ce^t))	\frac{d}{dt}(\frac{ce^{t}}{1+ce^{t}})
(dy)/(dt)=((y+1))/((t+1))	\frac{dy}{dt}=\frac{(y+1)}{(t+1)}
integral from 4 to 9 of (x-3)/(sqrt(x))	\int\:_{4}^{9}\frac{x-3}{\sqrt{x}}dx
integral of sec^4(xta)n^2x	\int\:\sec^{4}(xta)n^{2}xdx
integral of x/(sqrt(1+x))	\int\:\frac{x}{\sqrt{1+x}}dx
limit as x approaches 1 of 1/((x-1))	\lim\:_{x\to\:1}(\frac{1}{(x-1)})
integral of 5sin(2t)	\int\:5\sin(2t)dt
derivative of f(3)=-2/((x-2)^2)	derivative\:f(3)=-\frac{2}{(x-2)^{2}}
(d^2)/(dx^2)(5x^2)	\frac{d^{2}}{dx^{2}}(5x^{2})
(\partial)/(\partial z)(sin(y)cos(x))	\frac{\partial\:}{\partial\:z}(\sin(y)\cos(x))
derivative of arctanh(\sqrt[4]{x})	\frac{d}{dx}(\arctanh(\sqrt[4]{x}))
derivative of 2x-17	derivative\:2x-17
integral of sin(t)-cos(t)	\int\:\sin(t)-\cos(t)dt
limit as x approaches 2 of ln(x-2)	\lim\:_{x\to\:2}(\ln(x-2))
limit as x approaches-1 of 30	\lim\:_{x\to\:-1}(30)
(\partial)/(\partial x)(3x^2y^2-3)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}-3)
derivative of (2-x-3x^3)(7+x^5)	derivative\:(2-x-3x^{3})(7+x^{5})
derivative of (s^{(-1)/2}+7s)(1-s^{-1})	derivative\:(s^{\frac{-1}{2}}+7s)(1-s^{-1})
derivative of (2-x^3^3)	\frac{d}{dx}((2-x^{3})^{3})
limit as x approaches-3 of sqrt(19+x)	\lim\:_{x\to\:-3}(\sqrt{19+x})
tangent of x^2e^x-2xe^x+2e^x	tangent\:x^{2}e^{x}-2xe^{x}+2e^{x}
derivative of sin(x-x^2)	\frac{d}{dx}(\sin(x-x^{2}))
integral of 5sin^4(x)cos^2(x)	\int\:5\sin^{4}(x)\cos^{2}(x)dx
integral of 3/(50+2x)	\int\:\frac{3}{50+2x}dx

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