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Popular Calculus Problems

integral of y/(sqrt(16+y^2))	\int\:\frac{y}{\sqrt{16+y^{2}}}dy
x^5+y^4sqrt(x^6+4)y^'=0	x^{5}+y^{4}\sqrt{x^{6}+4}y^{\prime\:}=0
(\partial)/(\partial x)(-6e^xcos(yz))	\frac{\partial\:}{\partial\:x}(-6e^{x}\cos(yz))
limit as x approaches 1 of (x^4-6x^2+8x-3)/(x^4-2x^3+2x-1)	\lim\:_{x\to\:1}(\frac{x^{4}-6x^{2}+8x-3}{x^{4}-2x^{3}+2x-1})
integral from 0 to 2 of 2pi(9-x)(8-x^3)	\int\:_{0}^{2}2π(9-x)(8-x^{3})dx
integral from 120 to 150 of 0.1281xe^{-x/(100)}	\int\:_{120}^{150}0.1281\cdot\:x\cdot\:e^{-\frac{x}{100}}dx
4y+y^{''}=0	4y+y^{\prime\:\prime\:}=0
derivative of (1/(x^2)-3/(x^4))(x+9x^3)	derivative\:(\frac{1}{x^{2}}-\frac{3}{x^{4}})(x+9x^{3})
integral of 2/((1+x^2)^2)	\int\:\frac{2}{(1+x^{2})^{2}}dx
(d^2y)/(dt^2)+10(dy)/(dt)+25y=0	\frac{d^{2}y}{dt^{2}}+10\frac{dy}{dt}+25y=0
derivative of (x^3y+xy^3/(x^2+y^2))	\frac{d}{dx}(\frac{x^{3}y+xy^{3}}{x^{2}+y^{2}})
tangent of f(x)=sqrt(x-4),(13,3)	tangent\:f(x)=\sqrt{x-4},(13,3)
tangent of f(x)= 5/(x+1),\at x=(-1)/3	tangent\:f(x)=\frac{5}{x+1},\at\:x=\frac{-1}{3}
limit as x approaches 0 of (0+5)/(3(0))	\lim\:_{x\to\:0}(\frac{0+5}{3(0)})
derivative of f(x)=(x^2+8x+3)/(sqrt(x))	derivative\:f(x)=\frac{x^{2}+8x+3}{\sqrt{x}}
limit as x approaches infinity of (x^2+2x+5)/(e^{3x)}	\lim\:_{x\to\:\infty\:}(\frac{x^{2}+2x+5}{e^{3x}})
derivative of e^xcos(x+e^xsin(x))	\frac{d}{dx}(e^{x}\cos(x)+e^{x}\sin(x))
integral of (sin^2(3x))/(cos(3x))	\int\:\frac{\sin^{2}(3x)}{\cos(3x)}dx
integral of 1/((169-x^2)^{3/2)}	\int\:\frac{1}{(169-x^{2})^{\frac{3}{2}}}dx
taylor 1-x^3	taylor\:1-x^{3}
area 6x^2,x^2+5	area\:6x^{2},x^{2}+5
integral of-1/u	\int\:-\frac{1}{u}du
integral of ((x+4)(x-7))/(x^2)	\int\:\frac{(x+4)(x-7)}{x^{2}}dx
(\partial)/(\partial x)(sqrt((x+5)/(y+4)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x+5}{y+4}})
integral of 1/(9x^2+1)	\int\:\frac{1}{9x^{2}+1}dx
integral of sin(x	\int\:\sin(d)xdx
derivative of (x^3+1/(x^3-1))	\frac{d}{dx}(\frac{x^{3}+1}{x^{3}-1})
integral of (x-1)sqrt(2-x)	\int\:(x-1)\sqrt{2-x}dx
limit as x approaches 3 of (f(x)-f(pi))/(sqrt(x)-\sqrt{3)}	\lim\:_{x\to\:3}(\frac{f(x)-f(π)}{\sqrt{x}-\sqrt{3}})
integral from-infinity to infinity of x^8e^{-x^9}	\int\:_{-\infty\:}^{\infty\:}x^{8}e^{-x^{9}}dx
integral of-4sqrt(x)	\int\:-4\sqrt{x}dx
integral of-cos(x^2)	\int\:-\cos(x^{2})dx
(2x+3)^'	(2x+3)^{\prime\:}
derivative of In(x^3+x)	\frac{d}{dx}(In(x^{3}+x))
derivative of f(x)=2x^2+7x	derivative\:f(x)=2x^{2}+7x
derivative of x^4+7e^x	derivative\:x^{4}+7e^{x}
tangent of y=e^{3x},\at x= 1/3 ln(5)	tangent\:y=e^{3x},\at\:x=\frac{1}{3}\ln(5)
(\partial)/(\partial x)((5x)/(2y))	\frac{\partial\:}{\partial\:x}(\frac{5x}{2y})
integral from 0 to 1 of (e^{-0.2t})	\int\:_{0}^{1}(e^{-0.2t})dt
integral from 0 to 1 of sqrt(1+(\sqrt{2-x^2))^2}	\int\:_{0}^{1}\sqrt{1+(\sqrt{2-x^{2}})^{2}}dx
integral of arcsin(9x)	\int\:\arcsin(9x)dx
y^'+8y-6x=0	y^{\prime\:}+8y-6x=0
y^'= y/(y-x)	y^{\prime\:}=\frac{y}{y-x}
sum from n=1 to infinity of n^{-2.4}	\sum\:_{n=1}^{\infty\:}n^{-2.4}
integral of 1/(sqrt(1+y^2))	\int\:\frac{1}{\sqrt{1+y^{2}}}dy
integral from 1 to 4 of 8x-5	\int\:_{1}^{4}8x-5dx
(\partial)/(\partial x)(e^x)	\frac{\partial\:}{\partial\:x}(e^{x})
area X^2+X-12,X=0	area\:X^{2}+X-12,X=0
integral of-cos^{1/2}(3x)sin(3x)	\int\:-\cos^{\frac{1}{2}}(3x)\sin(3x)dx
(\partial)/(\partial y)(yx^{y-1})	\frac{\partial\:}{\partial\:y}(yx^{y-1})
y^{''}+6y^'+58y=0	y^{\prime\:\prime\:}+6y^{\prime\:}+58y=0
derivative of (-x^2/8)	\frac{d}{dx}(\frac{-x^{2}}{8})
integral of 1/((c^2+x^2))	\int\:\frac{1}{(c^{2}+x^{2})}dx
d/(dt)(2e^t)	\frac{d}{dt}(2e^{t})
integral of (11x^2)/((64+x^2)^2)	\int\:\frac{11x^{2}}{(64+x^{2})^{2}}dx
(dy)/(dx)+8y=9	\frac{dy}{dx}+8y=9
integral of xtan(2x)	\int\:x\tan(2x)dx
integral of (cos(7x))	\int\:(\cos(7x))dx
integral of tan^4(xse)c^4x	\int\:\tan^{4}(xse)c^{4}xdx
simplify t*e^{-t/2}	simplify\:t\cdot\:e^{-\frac{t}{2}}
derivative of 3x^2-6x+4	derivative\:3x^{2}-6x+4
d/(dt)(te^{at})	\frac{d}{dt}(te^{at})
(\partial)/(\partial y)(x^2y^3+2x^4y)	\frac{\partial\:}{\partial\:y}(x^{2}y^{3}+2x^{4}y)
derivative of sqrt(7-10x)	\frac{d}{dx}(\sqrt{7-10x})
integral of (sin(x))/(5+cos^2(x))	\int\:\frac{\sin(x)}{5+\cos^{2}(x)}dx
derivative of 1-\|1-x\|	\frac{d}{dx}(1-\left\|1-x\right\|)
integral of (x^4)/x	\int\:\frac{x^{4}}{x}dx
limit as x approaches 2 of sin(1/(x-2))	\lim\:_{x\to\:2}(\sin(\frac{1}{x-2}))
limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4))	\lim\:_{x\to\:\infty\:}(\frac{4x^{2}+5x}{\sqrt{10+x^{4}}})
3y^{''}-12y=0	3y^{\prime\:\prime\:}-12y=0
limit as x approaches 0+of 1/(x^3-2x^2)	\lim\:_{x\to\:0+}(\frac{1}{x^{3}-2x^{2}})
integral of cos((npix)/2)	\int\:\cos(\frac{nπx}{2})dx
limit as x approaches 3+of (sqrt(3))/(sqrt(x)-\sqrt{3)}-2x	\lim\:_{x\to\:3+}(\frac{\sqrt{3}}{\sqrt{x}-\sqrt{3}}-2x)
derivative of ln(3x+5y)	\frac{d}{dx}(\ln(3x+5y))
derivative of 1/(4x-7)	\frac{d}{dx}(\frac{1}{4x-7})
limit as x approaches 0+of (1+tan(x))^{3/x}	\lim\:_{x\to\:0+}((1+\tan(x))^{\frac{3}{x}})
derivative of arcsin(x+sqrt(1-x^2))	\frac{d}{dx}(\arcsin(x)+\sqrt{1-x^{2}})
derivative of f(x)=e^x-x^4	derivative\:f(x)=e^{x}-x^{4}
sum from n=1 to infinity of ln(n/(2n+5))	\sum\:_{n=1}^{\infty\:}\ln(\frac{n}{2n+5})
integral of (x^2-x+6)/(x^3+3x)	\int\:\frac{x^{2}-x+6}{x^{3}+3x}dx
(\partial)/(\partial x)((x*y)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{x\cdot\:y}{x+y})
(\partial)/(\partial x)(x^5+xy^7+4)	\frac{\partial\:}{\partial\:x}(x^{5}+xy^{7}+4)
derivative of (ln(x)^{ln(x)})	\frac{d}{dx}((\ln(x))^{\ln(x)})
limit as x approaches 7 of (x+4)/(x-7)	\lim\:_{x\to\:7}(\frac{x+4}{x-7})
derivative of f(2)=(x^2-4)/(x-2)	derivative\:f(2)=\frac{x^{2}-4}{x-2}
(d^2x)/(dt^2)=-kx	\frac{d^{2}x}{dt^{2}}=-kx
derivative of (8x^2-2x(5x+9))	\frac{d}{dx}((8x^{2}-2x)(5x+9))
y^{''}-4y^'+53y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+53y=0
derivative of (x^5+1^6)	\frac{d}{dx}((x^{5}+1)^{6})
derivative of Inbx^4	derivative\:Inbx^{4}
integral of 5e^x-3cosh(x)	\int\:5e^{x}-3\cosh(x)dx
integral of-(2x)/(x^2+1)	\int\:-\frac{2x}{x^{2}+1}dx
integral of-x^3+5x^2-4x	\int\:-x^{3}+5x^{2}-4xdx
limit as x approaches infinity of (\sqrt[3]{8x^9+x^6+2})/(4x^3+x^2-1)	\lim\:_{x\to\:\infty\:}(\frac{\sqrt[3]{8x^{9}+x^{6}+2}}{4x^{3}+x^{2}-1})
integral of cos(x)(6+4sin^2(x))	\int\:\cos(x)(6+4\sin^{2}(x))dx
limit as x approaches 2 of sqrt(3-x^2)	\lim\:_{x\to\:2}(\sqrt{3-x^{2}})
y^'=ysin(2x)	y^{\prime\:}=y\sin(2x)
limit as x approaches infinity of x(arctan(x)-pi/2)	\lim\:_{x\to\:\infty\:}(x(\arctan(x)-\frac{π}{2}))
derivative of f(x)=(7x^6+8x^3)^4	derivative\:f(x)=(7x^{6}+8x^{3})^{4}
4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=5	4y^{\prime\:\prime\:}-4y^{\prime\:}-3y=0,y(0)=1,y^{\prime\:}(0)=5

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