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Popular Calculus Problems

integral from 0 to 1 of sqrt(1+(6\sqrt{x))^2}	\int\:_{0}^{1}\sqrt{1+(6\sqrt{x})^{2}}dx
integral of (x^2-4x+3)/(x^3+2x^2+x)	\int\:\frac{x^{2}-4x+3}{x^{3}+2x^{2}+x}dx
(\partial)/(\partial x)(x+y+xy)	\frac{\partial\:}{\partial\:x}(x+y+xy)
limit as z approaches 2 of sqrt(7z^2+14z-7)	\lim\:_{z\to\:2}(\sqrt{7z^{2}+14z-7})
integral of 1/((x^2+3x-4))	\int\:\frac{1}{(x^{2}+3x-4)}dx
derivative of y=(3x^2+2)(4x-3)	derivative\:y=(3x^{2}+2)(4x-3)
inverse oflaplace 5/(s-3)-4/(s+6)	inverselaplace\:\frac{5}{s-3}-\frac{4}{s+6}
derivative of (2x+1/(3-x))	\frac{d}{dx}(\frac{2x+1}{3-x})
inverse oflaplace 1/(s^2(s+1))	inverselaplace\:\frac{1}{s^{2}(s+1)}
(d^4)/(dx^4)(arctan(x))	\frac{d^{4}}{dx^{4}}(\arctan(x))
integral of (x^3-10x-3)	\int\:(x^{3}-10x-3)dx
integral from 2 to 4 of ((6+x^2)/(x^3))	\int\:_{2}^{4}(\frac{6+x^{2}}{x^{3}})dx
limit as x approaches 0+of ln(x^2)	\lim\:_{x\to\:0+}(\ln(x^{2}))
derivative of ax^2+by(x^2)	\frac{d}{dx}(ax^{2}+by(x)^{2})
integral of (x^3+2x-1)	\int\:(x^{3}+2x-1)dx
derivative of a^3+cos^3(x)	derivative\:a^{3}+\cos^{3}(x)
area y=\|5x\|,y=x^2-6	area\:y=\left\|5x\right\|,y=x^{2}-6
derivative of ln(1-2x)	\frac{d}{dx}(\ln(1-2x))
(\partial)/(\partial θ)(-e^{-3r}sin(θ))	\frac{\partial\:}{\partial\:θ}(-e^{-3r}\sin(θ))
limit as x approaches infinity of 10	\lim\:_{x\to\:\infty\:}(10)
integral of 1/5-6/x	\int\:\frac{1}{5}-\frac{6}{x}dx
sum from n=1 to infinity of (n!)/(106^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{106^{n}}
d/(dt)(e^{3tsin(2t)})	\frac{d}{dt}(e^{3t\sin(2t)})
x^2y^{''}-3xy^'+5y=0,y(1)=-1,y^'(1)=4	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}+5y=0,y(1)=-1,y^{\prime\:}(1)=4
integral of sin(2x)*sin(x)	\int\:\sin(2x)\cdot\:\sin(x)dx
derivative of-(11/(sqrt(x)))	\frac{d}{dx}(-\frac{11}{\sqrt{x}})
integral of (5e^x)/(e^{2x)+8e^x+16}	\int\:\frac{5e^{x}}{e^{2x}+8e^{x}+16}dx
integral of (7/(x^4))	\int\:(\frac{7}{x^{4}})dx
(\partial)/(\partial x)(ln(e^x+y))	\frac{\partial\:}{\partial\:x}(\ln(e^{x}+y))
integral of (x+1)/((x-3)^2)	\int\:\frac{x+1}{(x-3)^{2}}dx
integral from t to 1 of 1/(x^2)	\int\:_{t}^{1}\frac{1}{x^{2}}dx
limit as x approaches 8 of cos((pix)/3)	\lim\:_{x\to\:8}(\cos(\frac{πx}{3}))
derivative of y=(x^4)/(f(x))	derivative\:y=\frac{x^{4}}{f(x)}
derivative of f(x)=3x^2-4x	derivative\:f(x)=3x^{2}-4x
y^{''}+2y^'+26y=0,y(0)=4,y^'(0)=-2	y^{\prime\:\prime\:}+2y^{\prime\:}+26y=0,y(0)=4,y^{\prime\:}(0)=-2
derivative of sqrt(x)*ln(x)	\frac{d}{dx}(\sqrt{x}\cdot\:\ln(x))
(\partial)/(\partial x)(x^{2+y^2})	\frac{\partial\:}{\partial\:x}(x^{2+y^{2}})
integral of (15x^4)	\int\:(15x^{4})dx
derivative of (-7x^2/(2x^2-5))	\frac{d}{dx}(\frac{-7x^{2}}{2x^{2}-5})
derivative of-cos(5x)	\frac{d}{dx}(-\cos(5x))
integral of 7e^4	\int\:7e^{4}dx
derivative of f(h)=x^2+2x+7	derivative\:f(h)=x^{2}+2x+7
2y^{''}+8y^'+8y=0	2y^{\prime\:\prime\:}+8y^{\prime\:}+8y=0
derivative of 5x^4e^x+e^xx^5	derivative\:5x^{4}e^{x}+e^{x}x^{5}
derivative of x^4-2x^2-8	\frac{d}{dx}(x^{4}-2x^{2}-8)
implicit (dy)/(dx),y=2^x	implicit\:\frac{dy}{dx},y=2^{x}
limit as x approaches 0 of (2x)/(3x)	\lim\:_{x\to\:0}(\frac{2x}{3x})
integral from 0 to 1 of 5^x	\int\:_{0}^{1}5^{x}dx
tangent of sqrt(sin(6x))	tangent\:\sqrt{\sin(6x)}
derivative of y= 1/((t^4+1)^3)	derivative\:y=\frac{1}{(t^{4}+1)^{3}}
(\partial)/(\partial y)((2x^2y)/(2+x^2y^2))	\frac{\partial\:}{\partial\:y}(\frac{2x^{2}y}{2+x^{2}y^{2}})
sum from n=0 to infinity of 1/(ln(n+2))	\sum\:_{n=0}^{\infty\:}\frac{1}{\ln(n+2)}
integral of x/(3x^2+4)	\int\:\frac{x}{3x^{2}+4}dx
limit as x approaches+3 of 2x^2-3x+4	\lim\:_{x\to\:+3}(2x^{2}-3x+4)
integral of 1/(x^{5/3)}	\int\:\frac{1}{x^{\frac{5}{3}}}dx
(\partial)/(\partial x)(200(x-y^2))	\frac{\partial\:}{\partial\:x}(200(x-y^{2}))
integral of tan(x)+3/2-3sin^2(x)	\int\:\tan(x)+\frac{3}{2}-3\sin^{2}(x)dx
derivative of x-cos(sqrt(x))	\frac{d}{dx}(x-\cos(\sqrt{x}))
derivative of (x+1(x^3+x-2))	\frac{d}{dx}((x+1)(x^{3}+x-2))
integral of 5/((x-1)(x^2+4))	\int\:\frac{5}{(x-1)(x^{2}+4)}dx
area 2x+1,(1,3)	area\:2x+1,(1,3)
8x^7y+x^8y^'=-5sec^2(x)tan(x)	8x^{7}y+x^{8}y^{\prime\:}=-5\sec^{2}(x)\tan(x)
derivative of-x+y+2	\frac{d}{dx}(-x+y+2)
limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6)	\lim\:_{x\to\:\frac{π}{6}}(\frac{\sin(x)-\sin(\frac{π}{6})}{x-\frac{π}{6}})
integral of 20tan(2x)sec^2(2x)	\int\:20\tan(2x)\sec^{2}(2x)dx
derivative of sin(ln(4x))	\frac{d}{dx}(\sin(\ln(4x)))
derivative of e^{-4x^2}	derivative\:e^{-4x^{2}}
limit as x approaches-1 of sqrt(16-4x)	\lim\:_{x\to\:-1}(\sqrt{16-4x})
integral of ((y)ln(1+y))	\int\:((y)\ln(1+y))dy
integral of (2+5/7 x-6x^2)	\int\:(2+\frac{5}{7}x-6x^{2})dx
derivative of (x-5sqrt(x-5))	\frac{d}{dx}((x-5)\sqrt{x-5})
limit as x approaches 0 of ((x-1)^3-1)/x	\lim\:_{x\to\:0}(\frac{(x-1)^{3}-1}{x})
integral of (2/x-1/(x^2))	\int\:(\frac{2}{x}-\frac{1}{x^{2}})dx
integral of 1/(x^2+10x-6)	\int\:\frac{1}{x^{2}+10x-6}dx
integral of tan^4(5x)	\int\:\tan^{4}(5x)dx
derivative of x^4+2e^x	derivative\:x^{4}+2e^{x}
limit as x approaches 2i of (x^2)/2	\lim\:_{x\to\:2i}(\frac{x^{2}}{2})
integral of 6xsin(x)	\int\:6x\sin(x)dx
integral of ((e^3)/(e^{x-1)})^2	\int\:(\frac{e^{3}}{e^{x-1}})^{2}dx
derivative of ((8x^2/(4-x))^3)	\frac{d}{dx}((\frac{8x^{2}}{4-x})^{3})
integral of csc^2(x)cot(x)	\int\:\csc^{2}(x)\cot(x)dx
derivative of 2xcos(2x)	\frac{d}{dx}(2x\cos(2x))
derivative of 4x^3+3x^2-6x	\frac{d}{dx}(4x^{3}+3x^{2}-6x)
y-x(dy)/(dx)=a(1+x^2(dy)/(dx))	y-x\frac{dy}{dx}=a(1+x^{2}\frac{dy}{dx})
tangent of f(x)=(5x-9)(x+5),(2,7)	tangent\:f(x)=(5x-9)(x+5),(2,7)
x^{''}+10x^'+21x=0	x^{\prime\:\prime\:}+10x^{\prime\:}+21x=0
integral of (x+10)/(x^2-x-2)	\int\:\frac{x+10}{x^{2}-x-2}dx
integral from-3 to 0 of (sqrt(9-x^2))	\int\:_{-3}^{0}(\sqrt{9-x^{2}})dx
(\partial)/(\partial x)(7y^6x^6-6y^5x^5)	\frac{\partial\:}{\partial\:x}(7y^{6}x^{6}-6y^{5}x^{5})
sqrt(y)dx+(x-4)dy=0	\sqrt{y}dx+(x-4)dy=0
derivative of e^{x^{-2}}	\frac{d}{dx}(e^{x^{-2}})
(\partial)/(\partial x)(-(4x)/((x^2-1)^2))	\frac{\partial\:}{\partial\:x}(-\frac{4x}{(x^{2}-1)^{2}})
inverse oflaplace 4/((s^2+4))	inverselaplace\:\frac{4}{(s^{2}+4)}
limit as x approaches infinity of csc(x)	\lim\:_{x\to\:\infty\:}(\csc(x))
3(dy)/(dx)=x^2	3\frac{dy}{dx}=x^{2}
integral of (x+8)/(3x^2-12)	\int\:\frac{x+8}{3x^{2}-12}dx
integral of (1/(x(ln(x)-1)))	\int\:(\frac{1}{x(\ln(x)-1)})dx
integral of (log_{3}(x))/(3x)	\int\:\frac{\log_{3}(x)}{3x}dx
integral of sin(4x)cos^2(2x)sin(x)	\int\:\sin(4x)\cos^{2}(2x)\sin(x)dx
derivative of tan(3)x^2	derivative\:\tan(3)x^{2}

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