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Popular Calculus Problems

limit as x approaches infinity of (4^x)/(5^{x+1)}	\lim\:_{x\to\:\infty\:}(\frac{4^{x}}{5^{x+1}})
integral of (2x+3)/(x(x-4)^2(x^2+2))	\int\:\frac{2x+3}{x(x-4)^{2}(x^{2}+2)}dx
integral of (x^2-9x+2)	\int\:(x^{2}-9x+2)dx
(d^2)/(dx^2)y+25y=0	\frac{d^{2}}{dx^{2}}y+25y=0
integral of 1/((x-7)(x+1))	\int\:\frac{1}{(x-7)(x+1)}dx
(\partial)/(\partial x)(6+3/x+6/(x^2))	\frac{\partial\:}{\partial\:x}(6+\frac{3}{x}+\frac{6}{x^{2}})
(x+ye^{y/x})dx=xe^{y/x}dy	(x+ye^{\frac{y}{x}})dx=xe^{\frac{y}{x}}dy
derivative of e^{3ln(x^2})	\frac{d}{dx}(e^{3\ln(x^{2})})
limit as x approaches 4 of-2x	\lim\:_{x\to\:4}(-2x)
inverse oflaplace 2/((s^2+4s+5)s)	inverselaplace\:\frac{2}{(s^{2}+4s+5)s}
integral of (1/((x-7)^2))	\int\:(\frac{1}{(x-7)^{2}})dx
limit as x approaches 0 of sin(-x^2)	\lim\:_{x\to\:0}(\sin(-x^{2}))
integral of pi(x^2-x^4)	\int\:π(x^{2}-x^{4})dx
factor 3t^2-3	factor\:3t^{2}-3
integral of y/(e^{2y)}	\int\:\frac{y}{e^{2y}}dy
limit as x approaches-1 of x^2+2	\lim\:_{x\to\:-1}(x^{2}+2)
integral of (sin(ln(y)))/y	\int\:\frac{\sin(\ln(y))}{y}dy
integral of 1/((1+x^2)^3)	\int\:\frac{1}{(1+x^{2})^{3}}dx
maclaurin 1/(1-x^3)	maclaurin\:\frac{1}{1-x^{3}}
(d^2)/(dx^2)(x^6-sqrt(x))	\frac{d^{2}}{dx^{2}}(x^{6}-\sqrt{x})
derivative of 5sin(x+4cos(x))	\frac{d}{dx}(5\sin(x)+4\cos(x))
integral of sec^4(4x)tan(4x)	\int\:\sec^{4}(4x)\tan(4x)dx
integral of 17z^3e^z	\int\:17z^{3}e^{z}dz
integral of xe^{x/4}	\int\:xe^{\frac{x}{4}}dx
integral of (3x^2)/(sqrt(4x-x^2))	\int\:\frac{3x^{2}}{\sqrt{4x-x^{2}}}dx
f(x)=sqrt(x^2+2)	f(x)=\sqrt{x^{2}+2}
(dy)/(dx)=sin(3x)	\frac{dy}{dx}=\sin(3x)
sum from k=1 to infinity of k/(2k+1)	\sum\:_{k=1}^{\infty\:}\frac{k}{2k+1}
y^{''}+y^'-72y=0	y^{\prime\:\prime\:}+y^{\prime\:}-72y=0
limit as x approaches 2-of (2x)/(x-1)	\lim\:_{x\to\:2-}(\frac{2x}{x-1})
(\partial)/(\partial x)(2sin(x))	\frac{\partial\:}{\partial\:x}(2\sin(x))
(dy)/(dx)=e^{3x}+8y	\frac{dy}{dx}=e^{3x}+8y
integral of-2/(x^2)	\int\:-\frac{2}{x^{2}}dx
integral from-4 to 4 of (e^x-e^{-x})^2	\int\:_{-4}^{4}(e^{x}-e^{-x})^{2}dx
(\partial)/(\partial y)((xy)^{1/2})	\frac{\partial\:}{\partial\:y}((xy)^{\frac{1}{2}})
integral of ((8x^2+3x-6))/((x^2-4)(x+2))	\int\:\frac{(8x^{2}+3x-6)}{(x^{2}-4)(x+2)}dx
(\partial)/(\partial y)(2arctan(x/y))	\frac{\partial\:}{\partial\:y}(2\arctan(\frac{x}{y}))
derivative of 2x^e	derivative\:2x^{e}
(dy)/(dx)=4y^2x	\frac{dy}{dx}=4y^{2}x
integral of cot(10x)	\int\:\cot(10x)dx
integral from 0 to 2 of (x/2)^3	\int\:_{0}^{2}(\frac{x}{2})^{3}dx
(\partial)/(\partial x)(ax^3+xe^x-1)	\frac{\partial\:}{\partial\:x}(ax^{3}+xe^{x}-1)
integral of (x^2+24)/(x(x-2)^3)	\int\:\frac{x^{2}+24}{x(x-2)^{3}}dx
derivative of (e^x/(7+e^x))	\frac{d}{dx}(\frac{e^{x}}{7+e^{x}})
integral of 1/((x+2)^2(x-4))	\int\:\frac{1}{(x+2)^{2}(x-4)}dx
derivative of cos(2arctan(x))	derivative\:\cos(2\arctan(x))
integral of sin(5x+pi/6)	\int\:\sin(5x+\frac{π}{6})dx
derivative of 1/2 x^2+8	derivative\:\frac{1}{2}x^{2}+8
derivative of y=pir^2	derivative\:y=πr^{2}
derivative of (e^x+x)^4	derivative\:(e^{x}+x)^{4}
(\partial)/(\partial x)(-1/((1+x)^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{(1+x)^{2}})
f(x)=pix^2	f(x)=πx^{2}
xy^{''}-4y^'=x^4	xy^{\prime\:\prime\:}-4y^{\prime\:}=x^{4}
derivative of 5arctan(3x)	\frac{d}{dx}(5\arctan(3x))
(\partial)/(\partial x)(x^2-2y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-2y^{2})
(\partial)/(\partial x)((x^2y^2)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}y^{2}}{x+y})
integral of (5x\sqrt[4]{6x^2+5})/4	\int\:\frac{5x\sqrt[4]{6x^{2}+5}}{4}dx
(\partial)/(\partial x)(30x^4y^5+24x^5y^7)	\frac{\partial\:}{\partial\:x}(30x^{4}y^{5}+24x^{5}y^{7})
tangent of f(x)= 1/((x-2))	tangent\:f(x)=\frac{1}{(x-2)}
derivative of cos(a^9+x^9)	derivative\:\cos(a^{9}+x^{9})
limit as x approaches 0 of cos(1/x)	\lim\:_{x\to\:0}(\cos(\frac{1}{x}))
integral from 0 to pi of 19cos^6(x)	\int\:_{0}^{π}19\cos^{6}(x)dx
derivative of (x+sqrt(2x)(2x+1))	\frac{d}{dx}((x+\sqrt{2x})(2x+1))
laplacetransform e^{(t-3)}	laplacetransform\:e^{(t-3)}
derivative of 4/((1-x^3))	\frac{d}{dx}(\frac{4}{(1-x)^{3}})
integral of (e^x)^3	\int\:(e^{x})^{3}dx
limit as x approaches pi of cos(x-pi)	\lim\:_{x\to\:π}(\cos(x-π))
tangent of f(x)=(3x)/(1+x^2),\at x=4	tangent\:f(x)=\frac{3x}{1+x^{2}},\at\:x=4
integral of 0.2+25x-200x^2+675x^3-900x^4+400x^5	\int\:0.2+25x-200x^{2}+675x^{3}-900x^{4}+400x^{5}dx
integral of 1/(x(2x+5)^2)	\int\:\frac{1}{x(2x+5)^{2}}dx
derivative of 25^x	\frac{d}{dx}(25^{x})
sum from n=0 to infinity of 8(-1/2)^n	\sum\:_{n=0}^{\infty\:}8(-\frac{1}{2})^{n}
derivative of 8x-2	\frac{d}{dx}(8x-2)
integral of 5cos(x)-csc^2(x)	\int\:5\cos(x)-\csc^{2}(x)dx
integral of x/(81x^4-1)	\int\:\frac{x}{81x^{4}-1}dx
integral from 1 to 4 of y^3+1/(4y^3)	\int\:_{1}^{4}y^{3}+\frac{1}{4y^{3}}dy
(\partial)/(\partial x)(1/(xsqrt(x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{x\sqrt{x}})
derivative of e^{x-5}-x	\frac{d}{dx}(e^{x-5}-x)
derivative of f(x)=((x^2))/((4+x))	derivative\:f(x)=\frac{(x^{2})}{(4+x)}
integral from 1 to 4 of t^2ln(4t)	\int\:_{1}^{4}t^{2}\ln(4t)dt
y^'+6y=t+e^{-4t}	y^{\prime\:}+6y=t+e^{-4t}
integral of (x^4+1)/(x(x^2+1)^2)	\int\:\frac{x^{4}+1}{x(x^{2}+1)^{2}}dx
(\partial)/(\partial x)(2x(x^2+1)^{-1})	\frac{\partial\:}{\partial\:x}(2x(x^{2}+1)^{-1})
derivative of e^{4x}	derivative\:e^{4x}
integral from 0 to 5 of 1/(x^{15/16)}	\int\:_{0}^{5}\frac{1}{x^{\frac{15}{16}}}dx
area y=6x^2ln(x),y=24ln(x)	area\:y=6x^{2}\ln(x),y=24\ln(x)
(\partial)/(\partial z)(xz-e^xsin(y))	\frac{\partial\:}{\partial\:z}(xz-e^{x}\sin(y))
derivative of f(x)=tan(3x)	derivative\:f(x)=\tan(3x)
derivative of ln(3x-1)	derivative\:\ln(3x-1)
sum from n=3 to infinity of 1/((2n-5)^3)	\sum\:_{n=3}^{\infty\:}\frac{1}{(2n-5)^{3}}
derivative of t^2sin(t)	derivative\:t^{2}\sin(t)
integral from 2 to 3 of 3/x	\int\:_{2}^{3}\frac{3}{x}dx
(\partial)/(\partial x)((8x)/(x^2+6y^2))	\frac{\partial\:}{\partial\:x}(\frac{8x}{x^{2}+6y^{2}})
integral of 13tan^3(θ)	\int\:13\tan^{3}(θ)dθ
limit as x approaches 0 of (sqrt(9+x))/x	\lim\:_{x\to\:0}(\frac{\sqrt{9+x}}{x})
sum from n=1 to infinity of 4-5/(2^n)	\sum\:_{n=1}^{\infty\:}4-\frac{5}{2^{n}}
derivative of ln(\sqrt[5]{x})	derivative\:\ln(\sqrt[5]{x})
integral of (e^{2x})/(2-e^{2x)}	\int\:\frac{e^{2x}}{2-e^{2x}}dx
y^{''}-1/t y^'+2/(t^2)y=0	y^{\prime\:\prime\:}-\frac{1}{t}y^{\prime\:}+\frac{2}{t^{2}}y=0
integral of xsqrt(4-3x^2)	\int\:x\sqrt{4-3x^{2}}dx

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