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Popular Calculus Problems

integral from 0 to 3 of (4-x^2)	\int\:_{0}^{3}(4-x^{2})dx
(dx)/(dt)=4x(7-x)	\frac{dx}{dt}=4x(7-x)
integral of 8/((x-4)^2)	\int\:\frac{8}{(x-4)^{2}}dx
limit as x approaches infinity of (x/(x+1))^{2x}	\lim\:_{x\to\:\infty\:}((\frac{x}{x+1})^{2x})
derivative of ax^3+bx^2	\frac{d}{dx}(ax^{3}+bx^{2})
derivative of g(x)=sqrt(9-x)	derivative\:g(x)=\sqrt{9-x}
(dy)/(dx)=(10x)/(3y)	\frac{dy}{dx}=\frac{10x}{3y}
integral of x^3e^{-x}	\int\:x^{3}e^{-x}dx
limit as x approaches 0 of x*csc(x)	\lim\:_{x\to\:0}(x\cdot\:\csc(x))
limit as x approaches 0 of 5x-2	\lim\:_{x\to\:0}(5x-2)
derivative of sin^2(e^{sin(2)(t)})	derivative\:\sin^{2}(e^{\sin(2)(t)})
derivative of 2cos^4(x)	\frac{d}{dx}(2\cos^{4}(x))
(dy)/(dx)=e^{-ax}-by,y(0)=0	\frac{dy}{dx}=e^{-a\cdot\:x}-b\cdot\:y,y(0)=0
limit as x approaches 10 of 1/((x-10)^2)	\lim\:_{x\to\:10}(\frac{1}{(x-10)^{2}})
d/(dθ)(r(θ)cos(θ))	\frac{d}{dθ}(r(θ)\cos(θ))
derivative of f(x)=(6x-4)^4	derivative\:f(x)=(6x-4)^{4}
limit as x approaches infinity of (pi/2-arctan(x))^{1/(ln(x))}	\lim\:_{x\to\:\infty\:}((\frac{π}{2}-\arctan(x))^{\frac{1}{\ln(x)}})
(\partial)/(\partial x)(5ye^{6x})	\frac{\partial\:}{\partial\:x}(5ye^{6x})
derivative of csc(10x)	\frac{d}{dx}(\csc(10x))
(\partial)/(\partial x)((x^5+x-y)^6)	\frac{\partial\:}{\partial\:x}((x^{5}+x-y)^{6})
derivative of y=9e^{-x}+e^{2x}	derivative\:y=9e^{-x}+e^{2x}
integral of 8x^3-cos(4x)	\int\:8x^{3}-\cos(4x)dx
d/(dh)((e^{ah}-1)/h)	\frac{d}{dh}(\frac{e^{ah}-1}{h})
integral of (x+1)ln(x+1)	\int\:(x+1)\ln(x+1)dx
integral of (e^{3x}+2)^2	\int\:(e^{3x}+2)^{2}dx
integral of 1/(x+5sqrt(x)+6)	\int\:\frac{1}{x+5\sqrt{x}+6}dx
derivative of sin(pi/6)	\frac{d}{dx}(\sin(\frac{π}{6}))
derivative of f(θ)=sqrt(5θ)	derivative\:f(θ)=\sqrt{5θ}
integral of (\sqrt[14]{x}+\sqrt[15]{x})	\int\:(\sqrt[14]{x}+\sqrt[15]{x})dx
tangent of f(x)=7x-4x^2,(-1,-11)	tangent\:f(x)=7x-4x^{2},(-1,-11)
tangent of f(x)= 5/(sqrt(x-7)),(8,5)	tangent\:f(x)=\frac{5}{\sqrt{x-7}},(8,5)
derivative of y=x^{16}	derivative\:y=x^{16}
(dy)/(dx)=x-2y	\frac{dy}{dx}=x-2y
(\partial)/(\partial x)(ln((x^2+y^2)/(x+y)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x^{2}+y^{2}}{x+y}))
limit as x approaches 1 of sqrt(4)	\lim\:_{x\to\:1}(\sqrt{4})
integral of (2x+3)^{-2}	\int\:(2x+3)^{-2}dx
y^'+3yx^5=0	y^{\prime\:}+3yx^{5}=0
sum from n=0 to infinity of 6/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{6}{4^{n}}
integral of xe^{x+y}	\int\:xe^{x+y}dx
derivative of x^3+x-2	\frac{d}{dx}(x^{3}+x-2)
limit as x approaches 2 of 5/x-8	\lim\:_{x\to\:2}(\frac{5}{x}-8)
integral of-x^2+2x+3	\int\:-x^{2}+2x+3dx
(dy)/(dx)=4x^3y-6x^2y	\frac{dy}{dx}=4x^{3}y-6x^{2}y
inverse oflaplace {(-3)/(-s+2)}	inverselaplace\:\left\{\frac{-3}{-s+2}\right\}
derivative of x^2y^{''}-9xy+25y	\frac{d}{dx}(x^{2}y^{\prime\:\prime\:}-9xy+25y)
integral of (e^x+e^{-x})	\int\:(e^{x}+e^{-x})dx
integral of (x^3)/(1-x^4)	\int\:\frac{x^{3}}{1-x^{4}}dx
area x=-5,x=1,y=11x,y=x^2-12	area\:x=-5,x=1,y=11x,y=x^{2}-12
tangent of 2x^4	tangent\:2x^{4}
inverse oflaplace (s+4)/(s^2+6s+25)	inverselaplace\:\frac{s+4}{s^{2}+6s+25}
derivative of (ln(3)+e^{x^e})^e	derivative\:(\ln(3)+e^{x^{e}})^{e}
limit as x approaches-1+of 1-x^2	\lim\:_{x\to\:-1+}(1-x^{2})
integral of 1/((1+x^2)(1+arctan(x)))	\int\:\frac{1}{(1+x^{2})(1+\arctan(x))}dx
limit as x approaches 7 of e^x-e^{-x}-x	\lim\:_{x\to\:7}(e^{x}-e^{-x}-x)
tangent of 9x^2+2x,\at x=3	tangent\:9x^{2}+2x,\at\:x=3
normal of y=x^3-3x+3,(2,5)	normal\:y=x^{3}-3x+3,(2,5)
derivative of sin(0)	\frac{d}{dx}(\sin(0))
derivative of 1/((x-1^2))	\frac{d}{dx}(\frac{1}{(x-1)^{2}})
derivative of \sqrt[3]{x}-3x	derivative\:\sqrt[3]{x}-3x
derivative of (4x^2+2x+4)/(sqrt(x))	derivative\:\frac{4x^{2}+2x+4}{\sqrt{x}}
(dy)/(dx)=e^{4x}+5y	\frac{dy}{dx}=e^{4x}+5y
limit as x approaches 0 of 5x^4	\lim\:_{x\to\:0}(5x^{4})
integral from 0 to 1 of 7xsqrt(x^2+16)	\int\:_{0}^{1}7x\sqrt{x^{2}+16}dx
derivative of sqrt(2)sin(x)	\frac{d}{dx}(\sqrt{2}\sin(x))
integral of 1/((4+x^2)^2)	\int\:\frac{1}{(4+x^{2})^{2}}dx
derivative of tan(sec(x))	derivative\:\tan(\sec(x))
integral from 3 to 4 of 1/6 (2x-3)	\int\:_{3}^{4}\frac{1}{6}(2x-3)dx
integral of sqrt(25-9x^2)	\int\:\sqrt{25-9x^{2}}dx
derivative of y=(sin(x))/(1+cos(x))	derivative\:y=\frac{\sin(x)}{1+\cos(x)}
derivative of 1/(\sqrt[3]{x^3+e^{-2/x}})	\frac{d}{dx}(\frac{1}{\sqrt[3]{x^{3}+e^{-\frac{2}{x}}}})
integral from 0 to 4 of \|4x-1\|	\int\:_{0}^{4}\left\|4x-1\right\|dx
integral of (6x^2)/(sqrt(4x-x^2))	\int\:\frac{6x^{2}}{\sqrt{4x-x^{2}}}dx
derivative of (4x^2+2x+4/(sqrt(x)))	\frac{d}{dx}(\frac{4x^{2}+2x+4}{\sqrt{x}})
sum from n=1 to infinity of 6^nx^nn!	\sum\:_{n=1}^{\infty\:}6^{n}x^{n}n!
integral of xcos(9x^2)	\int\:x\cos(9x^{2})dx
derivative of y=(3x^3-2)^5	derivative\:y=(3x^{3}-2)^{5}
inverse oflaplace (3e^{-4s})/(s+2)	inverselaplace\:\frac{3e^{-4s}}{s+2}
integral of (sqrt(x^2-25))/(x^2)	\int\:\frac{\sqrt{x^{2}-25}}{x^{2}}dx
integral of 3+(x^2+2)e^{x^3+6x}	\int\:3+(x^{2}+2)e^{x^{3}+6x}dx
integral of 8/(6+2sqrt(x))	\int\:\frac{8}{6+2\sqrt{x}}dx
(\partial)/(\partial x)(xe^{-t}sin(θ))	\frac{\partial\:}{\partial\:x}(xe^{-t}\sin(θ))
limit as x approaches 1 of (2/x-2)/(x-1)	\lim\:_{x\to\:1}(\frac{\frac{2}{x}-2}{x-1})
(\partial)/(\partial x)(e^x+e^{-x})	\frac{\partial\:}{\partial\:x}(e^{x}+e^{-x})
derivative of 3x^2+sqrt(x)+4	\frac{d}{dx}(3x^{2}+\sqrt{x}+4)
integral from 1 to 4 of x^{-3/2}	\int\:_{1}^{4}x^{-\frac{3}{2}}dx
integral from 0 to 4 of (5piy^4)/4	\int\:_{0}^{4}\frac{5πy^{4}}{4}dy
integral of (xcos(x^2))/(sqrt(sin(x^2)))	\int\:\frac{x\cos(x^{2})}{\sqrt{\sin(x^{2})}}dx
y^{''}+2sqrt(6)y^'+6y=0	y^{\prime\:\prime\:}+2\sqrt{6}y^{\prime\:}+6y=0
integral from 0 to 1 of (e^{2x}-e^x)	\int\:_{0}^{1}(e^{2x}-e^{x})dx
y^{''}+64y^'=0	y^{\prime\:\prime\:}+64y^{\prime\:}=0
integral from 1 to 3 of (x^2+2x)	\int\:_{1}^{3}(x^{2}+2x)dx
y^'+x^2sec(y)=0	y^{\prime\:}+x^{2}\sec(y)=0
derivative of-5	derivative\:-5
integral of sqrt(50+25e^{10t)+25e^{-10t}}	\int\:\sqrt{50+25e^{10t}+25e^{-10t}}dt
integral of (x-1)/(x+4)	\int\:\frac{x-1}{x+4}dx
integral of (2x-4)/(x^3+4x^2)	\int\:\frac{2x-4}{x^{3}+4x^{2}}dx
derivative of cos(sin(2x))	\frac{d}{dx}(\cos(\sin(2x)))
derivative of acos(7x+bsin(7x))	\frac{d}{dx}(a\cos(7x)+b\sin(7x))
sum from n=1 to infinity}(2^{-n of)/(5^{-n)}	\sum\:_{n=1}^{\infty\:}\frac{2^{-n}}{5^{-n}}
derivative of 5x+3	\frac{d}{dx}(5x+3)

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