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Popular Calculus Problems

integral of e^{3x-1}	\int\:e^{3x-1}dx
limit as x approaches-4 of x^2-5x+12	\lim\:_{x\to\:-4}(x^{2}-5x+12)
integral of-(sin(x))/(cos(x))	\int\:-\frac{\sin(x)}{\cos(x)}dx
integral of 3/(e^{2x)}	\int\:\frac{3}{e^{2x}}dx
integral from 0 to 1 of 8x^3	\int\:_{0}^{1}8x^{3}dx
integral from 0 to 4pi of t^2sin(t/2)	\int\:_{0}^{4π}t^{2}\sin(\frac{t}{2})dt
(dy)/(dx)=6+6y+x+xy	\frac{dy}{dx}=6+6y+x+xy
sum from n=1 to infinity of (2n)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{2n}{n+1}
integral of 32x^3-15x^2+8x	\int\:32x^{3}-15x^{2}+8xdx
integral of 2x^2sin(3x)	\int\:2x^{2}\sin(3x)dx
integral of ln((4x)^2)	\int\:\ln((4x)^{2})dx
integral of (10x)/(5x^2+1)	\int\:\frac{10x}{5x^{2}+1}dx
derivative of 1-1/(2sqrt(1-x))	\frac{d}{dx}(1-\frac{1}{2\sqrt{1-x}})
derivative of (x^2-6x+1)/(x^2+8)	derivative\:\frac{x^{2}-6x+1}{x^{2}+8}
derivative of 5+7sqrt(x)	derivative\:5+7\sqrt{x}
derivative of ln(xe^{sqrt(x)}+9)	derivative\:\ln(xe^{\sqrt{x}}+9)
tangent of f(x)= 1/(x^2),\at x=-1	tangent\:f(x)=\frac{1}{x^{2}},\at\:x=-1
limit as x approaches infinity of ln(5)	\lim\:_{x\to\:\infty\:}(\ln(5))
integral of ln(6x^4)	\int\:\ln(6x^{4})dx
integral from 0 to x of 1/x	\int\:_{0}^{x}\frac{1}{x}dx
derivative of 9cos^2(x)	\frac{d}{dx}(9\cos^{2}(x))
integral of 5x^2	\int\:5x^{2}dx
limit as x approaches 0 of (3-3)/x	\lim\:_{x\to\:0}(\frac{3-3}{x})
sum from k=1 to infinity of (2k+1)/k	\sum\:_{k=1}^{\infty\:}\frac{2k+1}{k}
(x+1)y^'+y=ln(x)	(x+1)y^{\prime\:}+y=\ln(x)
maclaurin (1+x)/(1-x)	maclaurin\:\frac{1+x}{1-x}
limit as x approaches 0+of (1+2x)^{1/x}	\lim\:_{x\to\:0+}((1+2x)^{\frac{1}{x}})
limit as x approaches 1.5 of 1/(x-2)	\lim\:_{x\to\:1.5}(\frac{1}{x-2})
xy^'+y=4xy^2,y(1)=9	xy^{\prime\:}+y=4xy^{2},y(1)=9
integral of-8e^{x+4}-5/(x+7)-5sec^2(x+6)	\int\:-8e^{x+4}-\frac{5}{x+7}-5\sec^{2}(x+6)dx
limit as x approaches-1+of x+4	\lim\:_{x\to\:-1+}(x+4)
(dx)/(dy)=xysin(y^2)	\frac{dx}{dy}=xy\sin(y^{2})
derivative of (2e^{-1/(x^2})/(x^3))	\frac{d}{dx}(\frac{2e^{-\frac{1}{x^{2}}}}{x^{3}})
(\partial)/(\partial z)(4z)	\frac{\partial\:}{\partial\:z}(4z)
integral of-tan(y)	\int\:-\tan(y)dy
integral of 1/(5-4cos(x))	\int\:\frac{1}{5-4\cos(x)}dx
ty^'=t+y	ty^{\prime\:}=t+y
derivative of y^2-cos(x)	\frac{d}{dx}(y^{2}-\cos(x))
inverse oflaplace ((s+5))/(s(s+4)^2)	inverselaplace\:\frac{(s+5)}{s(s+4)^{2}}
integral of (cos(x))/(5+sin^2(x))	\int\:\frac{\cos(x)}{5+\sin^{2}(x)}dx
(dy)/(dx)=6e^{x-y}	\frac{dy}{dx}=6e^{x-y}
derivative of sqrt(x^3)+x	\frac{d}{dx}(\sqrt{x^{3}}+x)
sum from n=1 to infinity of 1/(n^2+5)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+5}
integral of 1/(sqrt((4+x^2)))	\int\:\frac{1}{\sqrt{(4+x^{2})}}dx
derivative of y= 2/3 (x^2+1)^{3/2}	derivative\:y=\frac{2}{3}(x^{2}+1)^{\frac{3}{2}}
tangent of y=5xtan(x),\at x=pi	tangent\:y=5x\tan(x),\at\:x=π
derivative of f(x)=3^{x^5}	derivative\:f(x)=3^{x^{5}}
limit as x approaches 0+of x^{(1/x)}	\lim\:_{x\to\:0+}(x^{(\frac{1}{x})})
limit as x approaches 1-of x+3	\lim\:_{x\to\:1-}(x+3)
(dy)/(dt)+3y=13sin(2t),y(0)=6	\frac{dy}{dt}+3y=13\sin(2t),y(0)=6
tangent of f(x)=x^4+7x^2-x,(1,7)	tangent\:f(x)=x^{4}+7x^{2}-x,(1,7)
integral from 0 to 3 of (x^3-x)	\int\:_{0}^{3}(x^{3}-x)dx
x derivative of ln(y)=1	x\frac{d}{dx}(\ln(y))=1
limit as x approaches 2+of 1/(x+2)	\lim\:_{x\to\:2+}(\frac{1}{x+2})
derivative of 33(10sqrt(x)-x+10.45)	\frac{d}{dx}(33(10\sqrt{x}-x+10.45))
limit as x approaches 3+of (x-4)/(3-x)	\lim\:_{x\to\:3+}(\frac{x-4}{3-x})
d/(dt)(sqrt(5)t)	\frac{d}{dt}(\sqrt{5}t)
derivative of log_{10}(x+1)	derivative\:\log_{10}(x+1)
area y=-3x^2+6x+9,-3<= x<= 3	area\:y=-3x^{2}+6x+9,-3\le\:x\le\:3
derivative of sqrt(u)	derivative\:\sqrt{u}
tangent of f(x)=x^3-3x+1	tangent\:f(x)=x^{3}-3x+1
limit as n approaches infinity of x^{2n}	\lim\:_{n\to\:\infty\:}(x^{2n})
limit as x approaches o+of (x+1)^{inx}	\lim\:_{x\to\:o+}((x+1)^{inx})
limit as x approaches infinity of xe^{-sx}	\lim\:_{x\to\:\infty\:}(xe^{-sx})
derivative of (x^2-16/(x-4))	\frac{d}{dx}(\frac{x^{2}-16}{x-4})
integral of (x^2+10x+2)/(x^3+15x^2+6x+9)	\int\:\frac{x^{2}+10x+2}{x^{3}+15x^{2}+6x+9}dx
f(x)=3-2x	f(x)=3-2x
limit as x approaches 0 of tan(2x)csc(4x)	\lim\:_{x\to\:0}(\tan(2x)\csc(4x))
normal of y=x^4+5e^x,(0,5)	normal\:y=x^{4}+5e^{x},(0,5)
(dy)/(dx)=piy+12e	\frac{dy}{dx}=πy+12e
limit as x approaches pi of (5x)/3	\lim\:_{x\to\:π}(\frac{5x}{3})
area y=sqrt(x),y=x	area\:y=\sqrt{x},y=x
derivative of 3^{x^2-2x+1}	derivative\:3^{x^{2}-2x+1}
integral of y^2e^{-y}	\int\:y^{2}e^{-y}dy
derivative of y=(10)/x	derivative\:y=\frac{10}{x}
derivative of tan(x/2-cot(x/2))	\frac{d}{dx}(\tan(\frac{x}{2})-\cot(\frac{x}{2}))
integral of (2x-3)(4x^2+1)	\int\:(2x-3)(4x^{2}+1)dx
derivative of (5x/(x-2))	\frac{d}{dx}(\frac{5x}{x-2})
limit as x approaches-2 of 7/(x^2)	\lim\:_{x\to\:-2}(\frac{7}{x^{2}})
limit as x approaches 7-of ((x+8))/(x-7)	\lim\:_{x\to\:7-}(\frac{(x+8)}{x-7})
integral of sin(2x)*cos(x)	\int\:\sin(2x)\cdot\:\cos(x)dx
derivative of x^3-3x^2+2x	\frac{d}{dx}(x^{3}-3x^{2}+2x)
(\partial)/(\partial x)(x^3y^3+y-z+3)	\frac{\partial\:}{\partial\:x}(x^{3}y^{3}+y-z+3)
(\partial)/(\partial x)(x^7y^8-x^6y^7)	\frac{\partial\:}{\partial\:x}(x^{7}y^{8}-x^{6}y^{7})
laplacetransform e^{-2t}sin(3t)	laplacetransform\:e^{-2t}\sin(3t)
integral of xcsc^2(x)	\int\:x\csc^{2}(x)dx
limit as x approaches+(-2) of (-9)/(x^2)	\lim\:_{x\to\:+(-2)}(\frac{-9}{x^{2}})
2<= x<= 6,y=2	2\le\:x\le\:6,y=2
derivative of x^4cos(7x-5)	derivative\:x^{4}\cos(7x-5)
derivative of 2ay	derivative\:2ay
critical f(x)=e^{y^2}+2x^3	critical\:f(x)=e^{y^{2}}+2x^{3}
(\partial)/(\partial y)(2cos(x+2y))	\frac{\partial\:}{\partial\:y}(2\cos(x+2y))
integral of (x^2-4)/(x(x^2+4))	\int\:\frac{x^{2}-4}{x(x^{2}+4)}dx
integral of cos^5(θ)sin(θ)	\int\:\cos^{5}(θ)\sin(θ)dθ
area y=x,y=2xsqrt(49-x^2)	area\:y=x,y=2x\sqrt{49-x^{2}}
y^{''}+25y=0,y(pi)=3,y^'(pi)=-3	y^{\prime\:\prime\:}+25y=0,y(π)=3,y^{\prime\:}(π)=-3
integral from 0 to 4 of (-x^2+4x)	\int\:_{0}^{4}(-x^{2}+4x)dx
slope of (1)(-1.5)	slope\:(1)(-1.5)
y^'+3y=2e^{-x}	y^{\prime\:}+3y=2e^{-x}
integral of 1/(x(x^2-4))	\int\:\frac{1}{x(x^{2}-4)}dx

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