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Popular Calculus Problems

integral of (e^xx)/(x^2)	\int\:\frac{e^{x}x}{x^{2}}dx
integral from 0 to 1 of (10y)/(e^{2y)}	\int\:_{0}^{1}\frac{10y}{e^{2y}}dy
derivative of 4xsin(xcos(x))	\frac{d}{dx}(4x\sin(x)\cos(x))
(dy)/(dx)=7x^2-xy	\frac{dy}{dx}=7x^{2}-xy
(\partial)/(\partial x)(e^{-8y}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-8y}\cos(πx))
tangent of x^3-3x+1(3.19)	tangent\:x^{3}-3x+1(3.19)
integral of tan^8(x)sec^2(x)	\int\:\tan^{8}(x)\sec^{2}(x)dx
xy^'=-y-x,y(1)=1	xy^{\prime\:}=-y-x,y(1)=1
limit as x approaches-2 of (-x)/(-x+2)	\lim\:_{x\to\:-2}(\frac{-x}{-x+2})
derivative of (7x)^x	derivative\:(7x)^{x}
integral of (2x+5)/(x^2+x)	\int\:\frac{2x+5}{x^{2}+x}dx
integral of ((1-2/3 x^2)^6)(x)	\int\:((1-\frac{2}{3}x^{2})^{6})(x)dx
(\partial)/(\partial y)(sqrt(x^2+y^2-1))	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}+y^{2}-1})
derivative of (x^2-5x+1(2x+3))	\frac{d}{dx}((x^{2}-5x+1)(2x+3))
(\partial)/(\partial y)(((ax+by))/(cx+dy))	\frac{\partial\:}{\partial\:y}(\frac{(ax+by)}{cx+dy})
y^{''}=e^{(3t)}	y^{\prime\:\prime\:}=e^{(3t)}
area-x^2+5x,x^2-3x	area\:-x^{2}+5x,x^{2}-3x
integral from 4 to 5 of x/(x^2+6x+13)	\int\:_{4}^{5}\frac{x}{x^{2}+6x+13}dx
(\partial)/(\partial x)(6x)	\frac{\partial\:}{\partial\:x}(6x)
(\partial)/(\partial x)((A^2x^2+B^2y^2)^4)	\frac{\partial\:}{\partial\:x}((A^{2}x^{2}+B^{2}y^{2})^{4})
(\partial)/(\partial x)(a(x-b))	\frac{\partial\:}{\partial\:x}(a(x-b))
integral of (2sqrt(x)+5)/x	\int\:\frac{2\sqrt{x}+5}{x}dx
integral from 0 to 16 of xsqrt(16-x)	\int\:_{0}^{16}x\sqrt{16-x}dx
integral from 0 to infinity of x/(x^3+1)	\int\:_{0}^{\infty\:}\frac{x}{x^{3}+1}dx
limit as x approaches 3 of (4x-5)/(5x-1)	\lim\:_{x\to\:3}(\frac{4x-5}{5x-1})
integral of+x^2sqrt(x^3+27)	\int\:+x^{2}\sqrt{x^{3}+27}dx
inverse oflaplace (2se^{-3s})/(3s^2+27)	inverselaplace\:\frac{2se^{-3s}}{3s^{2}+27}
derivative of 1/(sqrt(1-x^2-y))	\frac{d}{dx}(\frac{1}{\sqrt{1-x^{2}-y}})
integral of (e^{4/t})/(t^2)	\int\:\frac{e^{\frac{4}{t}}}{t^{2}}dt
derivative of (8-xe^x/(x+e^x))	\frac{d}{dx}(\frac{8-xe^{x}}{x+e^{x}})
integral of+1/(sqrt(-x^2+8x-15))	\int\:+\frac{1}{\sqrt{-x^{2}+8x-15}}dx
derivative of ((x^2)/(e^{2x)})^6	derivative\:(\frac{x^{2}}{e^{2x}})^{6}
derivative of-7sqrt(x)+3/(x^6)	derivative\:-7\sqrt{x}+\frac{3}{x^{6}}
(dy)/(dx)=e^{3x-2y}	\frac{dy}{dx}=e^{3x-2y}
derivative of sqrt({f)(x}-4x+1)	\frac{d}{dx}(\sqrt{{f}(x)}-4x+1)
sum from n=1 to infinity of (10/11)^n	\sum\:_{n=1}^{\infty\:}(\frac{10}{11})^{n}
derivative of f(x)=-x-1/x	derivative\:f(x)=-x-\frac{1}{x}
derivative of e^{(x-1})	\frac{d}{dx}(e^{(x-1)})
derivative of (8x^2-40x+32/(3x^{1/3)})	\frac{d}{dx}(\frac{8x^{2}-40x+32}{3x^{\frac{1}{3}}})
derivative of (x^2/(x^2+2x-15))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+2x-15})
integral of 5xsin^2(x)	\int\:5x\sin^{2}(x)dx
(\partial)/(\partial x)(sin(2x)cos(2y))	\frac{\partial\:}{\partial\:x}(\sin(2x)\cos(2y))
maclaurin (x^2)/(1-x^2)	maclaurin\:\frac{x^{2}}{1-x^{2}}
integral of 15x^{1/2}	\int\:15x^{\frac{1}{2}}dx
integral from-2 to 2 of \|x^2+3x-4\|	\int\:_{-2}^{2}\left\|x^{2}+3x-4\right\|dx
y^'-6/x y=(y^4)/(x^7)	y^{\prime\:}-\frac{6}{x}y=\frac{y^{4}}{x^{7}}
integral of 4x^3(7x^4+12)^3	\int\:4x^{3}(7x^{4}+12)^{3}dx
derivative of (6x^2+4x)^2	derivative\:(6x^{2}+4x)^{2}
(\partial)/(\partial y)((x-y)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{x-y}{x^{2}+y^{2}})
derivative of 3e^t	derivative\:3e^{t}
integral of csc^2(θ)	\int\:\csc^{2}(θ)dθ
derivative of f(θ)=cot(θ)	derivative\:f(θ)=\cot(θ)
integral of 1/(u^2+4)	\int\:\frac{1}{u^{2}+4}du
limit as x approaches 0+of (5x)^x	\lim\:_{x\to\:0+}((5x)^{x})
limit as x approaches infinity of 1/x-1	\lim\:_{x\to\:\infty\:}(\frac{1}{x}-1)
integral of-6tan^2(x)	\int\:-6\tan^{2}(x)dx
x^3(dy)/(dx)+(2-3x^2)y=x^3	x^{3}\frac{dy}{dx}+(2-3x^{2})y=x^{3}
limit as x approaches 1 of (x^3)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{3}}{x-1})
inverse oflaplace 2/(s-3)	inverselaplace\:\frac{2}{s-3}
tangent of f(x)=x^2+2,(5,27)	tangent\:f(x)=x^{2}+2,(5,27)
derivative of 10sin(x)cos(x)	derivative\:10\sin(x)\cos(x)
implicit (dy)/(dx),y=3x^2	implicit\:\frac{dy}{dx},y=3x^{2}
(\partial)/(\partial x)(-(sqrt(x^2+y^2)))	\frac{\partial\:}{\partial\:x}(-(\sqrt{x^{2}+y^{2}}))
derivative of ln(xe^{-8x})	derivative\:\ln(xe^{-8x})
area y=x^4-2x^3,y=0	area\:y=x^{4}-2x^{3},y=0
integral of e^{-x}e^x	\int\:e^{-x}e^{x}dx
integral from 0 to infinity of e^{-st}t	\int\:_{0}^{\infty\:}e^{-st}tdt
integral of (1+x)sqrt(x)	\int\:(1+x)\sqrt{x}dx
tangent of f(x)=9e^xcos(x),(0,9)	tangent\:f(x)=9e^{x}\cos(x),(0,9)
y^{''}+y=x^3	y^{\prime\:\prime\:}+y=x^{3}
integral from 0 to y of ye^{-y}	\int\:_{0}^{y}ye^{-y}dy
(dy)/(dt)y=(2t-1)(3t-4)^{-1}	\frac{dy}{dt}y=(2t-1)(3t-4)^{-1}
derivative of log_{5}(2x)	derivative\:\log_{5}(2x)
integral from-pi/4 to pi/4 of tan(x)	\int\:_{-\frac{π}{4}}^{\frac{π}{4}}\tan(x)dx
integral of 2sin(x)cos^2(x)	\int\:2\sin(x)\cos^{2}(x)dx
integral of (sqrt(9x^2-16))/x	\int\:\frac{\sqrt{9x^{2}-16}}{x}dx
derivative of f(x)=4^{(x^9)}	derivative\:f(x)=4^{(x^{9})}
sum from n=0 to infinity of 1/(1+n)	\sum\:_{n=0}^{\infty\:}\frac{1}{1+n}
derivative of sqrt(x)(x^3+x^2-3x)	\frac{d}{dx}(\sqrt{x}(x^{3}+x^{2}-3x))
integral of (2x+3)/(x^3+3x)	\int\:\frac{2x+3}{x^{3}+3x}dx
derivative of (4x/(4+sqrt(x)))	\frac{d}{dx}(\frac{4x}{4+\sqrt{x}})
integral of 1/(e^x+2)	\int\:\frac{1}{e^{x}+2}dx
derivative of e^{-x^2}-sin(xcos(x))	\frac{d}{dx}(e^{-x^{2}}-\sin(x)\cos(x))
(\partial)/(\partial x)(ln(2x^3+y))	\frac{\partial\:}{\partial\:x}(\ln(2x^{3}+y))
derivative of f(x)=(-25x^2+9)^2	derivative\:f(x)=(-25x^{2}+9)^{2}
(\partial)/(\partial x)(1-x-y)	\frac{\partial\:}{\partial\:x}(1-x-y)
inverse oflaplace 4/(s+2)	inverselaplace\:\frac{4}{s+2}
integral of (2000)/(1+0.3e^{-0.276t)}	\int\:\frac{2000}{1+0.3e^{-0.276t}}dt
(\partial)/(\partial x)((xyz)^{1/2})	\frac{\partial\:}{\partial\:x}((xyz)^{\frac{1}{2}})
integral of (5x^2-3)(2x)	\int\:(5x^{2}-3)(2x)dx
integral of (7x+6)^4	\int\:(7x+6)^{4}dx
(\partial)/(\partial y)(2x+ye^{xy})	\frac{\partial\:}{\partial\:y}(2x+ye^{xy})
limit as t approaches 0 of 6/t-6/(t^2+t)	\lim\:_{t\to\:0}(\frac{6}{t}-\frac{6}{t^{2}+t})
integral of-2^{-x}	\int\:-2^{-x}dx
sum from n=1 to infinity of 1/(3^{n-1)}	\sum\:_{n=1}^{\infty\:}\frac{1}{3^{n-1}}
derivative of (16/x)	\frac{d}{dx}(\frac{16}{x})
y^{''}-3y^'=-9	y^{\prime\:\prime\:}-3y^{\prime\:}=-9
integral of (x^3)/(sqrt(25-x^2))	\int\:\frac{x^{3}}{\sqrt{25-x^{2}}}dx
integral from 0 to 2 of 3ysqrt(4-y^2)	\int\:_{0}^{2}3y\sqrt{4-y^{2}}dy
y^{''}+y^'-6y=0,y(0)=3	y^{\prime\:\prime\:}+y^{\prime\:}-6y=0,y(0)=3

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