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Popular Calculus Problems

integral of 8sec^4(θ)tan^2(θ)	\int\:8\sec^{4}(θ)\tan^{2}(θ)dθ
(\partial)/(\partial x)(xy+1/x+8/y)	\frac{\partial\:}{\partial\:x}(xy+\frac{1}{x}+\frac{8}{y})
sum from n=1 to infinity of 1/((3+2n)^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{(3+2n)^{2}}
integral from 1 to infinity of 21(e-sqrt(x))/(sqrt(x))	\int\:_{1}^{\infty\:}21\frac{e-\sqrt{x}}{\sqrt{x}}dx
integral of-3ln(2x+1)	\int\:-3\ln(2x+1)dx
derivative of 7e^xarctan(x)	derivative\:7e^{x}\arctan(x)
t^2y^{''}-2ty^'-4y=0	t^{2}y^{\prime\:\prime\:}-2ty^{\prime\:}-4y=0
derivative of (d/(dx(2))/x)	\frac{d}{dx}(\frac{\frac{d}{dx}(2)}{x})
derivative of y=4e^x+4ln(x)	derivative\:y=4e^{x}+4\ln(x)
derivative of 100xy	\frac{d}{dx}(100xy)
derivative of x^3*e^{-3x}	\frac{d}{dx}(x^{3}\cdot\:e^{-3x})
integral of ((x+2)/(x^2+4x))	\int\:(\frac{x+2}{x^{2}+4x})dx
integral of ((7^x))/(sqrt(1-7^{2x))}	\int\:\frac{(7^{x})}{\sqrt{1-7^{2x}}}dx
integral of e^{-3}	\int\:e^{-3}dx
taylor ln(1-x^2)	taylor\:\ln(1-x^{2})
integral of (x^2+2x-3)	\int\:(x^{2}+2x-3)dx
integral from 0 to 1 of (1+12t)/(1+3t)	\int\:_{0}^{1}\frac{1+12t}{1+3t}dt
(-6sin(6x))^'	(-6\sin(6x))^{\prime\:}
integral of (-5e^x+4/x)	\int\:(-5e^{x}+\frac{4}{x})dx
d/(dy)(xy^2)	\frac{d}{dy}(xy^{2})
integral of tsin(kt)	\int\:t\sin(kt)dt
integral of 1/(y^2sqrt(y^2+16))	\int\:\frac{1}{y^{2}\sqrt{y^{2}+16}}dy
derivative of 4x^{5/4}+10x^{3/2}+8x	derivative\:4x^{\frac{5}{4}}+10x^{\frac{3}{2}}+8x
limit as x approaches 0-of (1+x)^{1/(x^2)}	\lim\:_{x\to\:0-}((1+x)^{\frac{1}{x^{2}}})
integral of 1+(2x^2+x+6)/((x^2-1)(x-2))	\int\:1+\frac{2x^{2}+x+6}{(x^{2}-1)(x-2)}dx
x^2y^{''}+2xy^'=0	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}=0
integral of sin^2(2x)*cos(2x)	\int\:\sin^{2}(2x)\cdot\:\cos(2x)dx
derivative of x^5e^{2x}	derivative\:x^{5}e^{2x}
(\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y))	\frac{\partial\:}{\partial\:x}(e^{-3πt}\cos(4x)\sin(6y))
derivative of y=in(x)	derivative\:y=in(x)
integral of tec(2t)	\int\:tec(2t)dt
derivative of (x+1*(x^2-1))	\frac{d}{dx}((x+1)\cdot\:(x^{2}-1))
derivative of (x^2-3)/(x-2)	derivative\:\frac{x^{2}-3}{x-2}
derivative of y=(5x^2-6x)^{-2}	derivative\:y=(5x^{2}-6x)^{-2}
integral of (sec(x)tan(x))/(sec(x)-6)	\int\:\frac{\sec(x)\tan(x)}{\sec(x)-6}dx
integral of x^2e^xsin(x)	\int\:x^{2}e^{x}\sin(x)dx
(\partial)/(\partial x)(xy+xe^{1/y})	\frac{\partial\:}{\partial\:x}(xy+xe^{\frac{1}{y}})
integral of sec^2(u)	\int\:\sec^{2}(u)du
integral of (32)/(x^2-64)	\int\:\frac{32}{x^{2}-64}dx
integral of ((ln(u))^4)/u	\int\:\frac{(\ln(u))^{4}}{u}du
integral of x^3cos(12x)	\int\:x^{3}\cos(12x)dx
limit as x approaches 0 of (x-1)/(x^2+1)	\lim\:_{x\to\:0}(\frac{x-1}{x^{2}+1})
integral from 2 to x of (t^3+8t-5)	\int\:_{2}^{x}(t^{3}+8t-5)dt
derivative of ae^xcos(x)	\frac{d}{dx}(ae^{x}\cos(x))
(\partial)/(\partial x)(((3x-3z))/(y+3z))	\frac{\partial\:}{\partial\:x}(\frac{(3x-3z)}{y+3z})
integral of 3cos(x)-2sin(x)	\int\:3\cos(x)-2\sin(x)dx
tangent of e^x+1,\at x=0	tangent\:e^{x}+1,\at\:x=0
area y=3+2sqrt(x),y=(9+x)/3	area\:y=3+2\sqrt{x},y=\frac{9+x}{3}
tangent of y=-2x^3,(-2,16)	tangent\:y=-2x^{3},(-2,16)
integral of (2y)/3	\int\:\frac{2y}{3}dy
tangent of f(x)=x^4+4x^2-x,\at x=1	tangent\:f(x)=x^{4}+4x^{2}-x,\at\:x=1
integral of sin^5(7x)cos^2(7x)	\int\:\sin^{5}(7x)\cos^{2}(7x)dx
derivative of 2sqrt(x)-3\sqrt[3]{x}	\frac{d}{dx}(2\sqrt{x}-3\sqrt[3]{x})
derivative of asin(x+bcos(x))	\frac{d}{dx}(a\sin(x)+b\cos(x))
integral of (ln(x^7))/x	\int\:\frac{\ln(x^{7})}{x}dx
integral of 1/((4-x)^2)	\int\:\frac{1}{(4-x)^{2}}dx
(y)dx-(x+sqrt(y^2-x^2))dy=0	(y)dx-(x+\sqrt{y^{2}-x^{2}})dy=0
(ln(cos(x)))^'	(\ln(\cos(x)))^{\prime\:}
limit as x approaches 0 of (4tan(x))/x	\lim\:_{x\to\:0}(\frac{4\tan(x)}{x})
derivative of 1/(e^{-x^2})	\frac{d}{dx}(\frac{1}{e^{-x^{2}}})
integral of x(1+1/x)^3	\int\:x(1+\frac{1}{x})^{3}dx
limit as x approaches+1 of ln(3)+e^x	\lim\:_{x\to\:+1}(\ln(3)+e^{x})
integral of (2x^2+24)/(x(x-2)^3)	\int\:\frac{2x^{2}+24}{x(x-2)^{3}}dx
derivative of-x^2-3x+4	\frac{d}{dx}(-x^{2}-3x+4)
integral of 1/(a^2-u^2)	\int\:\frac{1}{a^{2}-u^{2}}du
θ^{''}+a/b*θ=0	θ^{\prime\:\prime\:}+\frac{a}{b}\cdot\:θ=0
integral from 2 to 5 of 1/x	\int\:_{2}^{5}\frac{1}{x}dx
tangent of x^2-1	tangent\:x^{2}-1
integral from 0 to 1 of (x^2+1)(e^{-x})	\int\:_{0}^{1}(x^{2}+1)(e^{-x})dx
inverse oflaplace 1/(s^2+4s+8)	inverselaplace\:\frac{1}{s^{2}+4s+8}
derivative of g(x)= 3/(sqrt(6x+8))	derivative\:g(x)=\frac{3}{\sqrt{6x+8}}
integral of x^2-2x-3	\int\:x^{2}-2x-3dx
(1-2y+x)(dy)/(dx)+y=2x-1	(1-2y+x)\frac{dy}{dx}+y=2x-1
integral of sin(1-2x)cos(1+2x)	\int\:\sin(1-2x)\cos(1+2x)dx
derivative of (8x^2-5x(13x^2+4))	\frac{d}{dx}((8x^{2}-5x)(13x^{2}+4))
(\partial)/(\partial x)(ce^{-x}sin(4x))	\frac{\partial\:}{\partial\:x}(ce^{-x}\sin(4x))
integral of 3te^t	\int\:3te^{t}dt
integral of (x^2)/(sqrt(x^3+3))	\int\:\frac{x^{2}}{\sqrt{x^{3}+3}}dx
integral of (sin(x))^2	\int\:(\sin(x))^{2}dx
sum from n=1 to infinity of (4/10)^n*3	\sum\:_{n=1}^{\infty\:}(\frac{4}{10})^{n}\cdot\:3
derivative of ln(cosh(8x))	\frac{d}{dx}(\ln(\cosh(8x)))
(d^2)/(dx^2)(x^2e^{-2x})	\frac{d^{2}}{dx^{2}}(x^{2}e^{-2x})
integral of 1/v	\int\:\frac{1}{v}dv
tangent of 1/16 tan^2(x)+cos(x)	tangent\:\frac{1}{16}\tan^{2}(x)+\cos(x)
integral of (x^2+10x-1)/(x^3-x)	\int\:\frac{x^{2}+10x-1}{x^{3}-x}dx
integral of-2ysqrt(2-y^2)	\int\:-2y\sqrt{2-y^{2}}dy
integral of 1/(p^2+2p)	\int\:\frac{1}{p^{2}+2p}dp
area x=y^2,x=y+6	area\:x=y^{2},x=y+6
derivative of csc(xcot(x))	\frac{d}{dx}(\csc(x)\cot(x))
derivative of x^{sqrt(2)}	derivative\:x^{\sqrt{2}}
area f(x)=-x^2+2,g(x)=-x-4	area\:f(x)=-x^{2}+2,g(x)=-x-4
integral of v^{-4/5}	\int\:v^{-\frac{4}{5}}dv
integral of 3/((3x-1)ln(3x-1))	\int\:\frac{3}{(3x-1)\ln(3x-1)}dx
integral of sin^6(ax)	\int\:\sin^{6}(ax)dx
derivative of arcsin(1-x)	\frac{d}{dx}(\arcsin(1-x))
integral from 3 to infinity of 1/(x^2+x)	\int\:_{3}^{\infty\:}\frac{1}{x^{2}+x}dx
integral of 2x(x^2+6)^9	\int\:2x(x^{2}+6)^{9}dx
derivative of arcsin(4-3x)	\frac{d}{dx}(\arcsin(4-3x))
t^2(dy)/(dt)+ty=6	t^{2}\frac{dy}{dt}+ty=6
sum from n=0 to infinity of n/3 (2/3)^n	\sum\:_{n=0}^{\infty\:}\frac{n}{3}(\frac{2}{3})^{n}

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