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Popular Calculus Problems

integral of 5x+12	\int\:5x+12dx
sum from n=0 to infinity of n*(1/6)^n	\sum\:_{n=0}^{\infty\:}n\cdot\:(\frac{1}{6})^{n}
xy^'+2y-2x^2y^2=0	xy^{\prime\:}+2y-2x^{2}y^{2}=0
derivative of f(x)=(2x-3)^4(x^2+x+1)^5	derivative\:f(x)=(2x-3)^{4}(x^{2}+x+1)^{5}
integral of 1/(sqrt(x^2+6x+13))	\int\:\frac{1}{\sqrt{x^{2}+6x+13}}dx
integral from 1 to 4 of 3e^{sqrt(x)}	\int\:_{1}^{4}3e^{\sqrt{x}}dx
derivative of tan(pi)	\frac{d}{dx}(\tan(π))
area x=1,y=6x(2-x^2)^2	area\:x=1,y=6x(2-x^{2})^{2}
limit as x approaches-4-of (-4x^3)/(4+x)	\lim\:_{x\to\:-4-}(\frac{-4x^{3}}{4+x})
limit as x approaches a+of x^n	\lim\:_{x\to\:a+}(x^{n})
integral of (x^6+4x^3+4)/(x^3-4x^2)	\int\:\frac{x^{6}+4x^{3}+4}{x^{3}-4x^{2}}dx
derivative of cos(x+x^5)	\frac{d}{dx}(\cos(x)+x^{5})
(dy)/(dx)+5xy=4x	\frac{dy}{dx}+5xy=4x
integral of (sqrt(x^2-16))/x	\int\:\frac{\sqrt{x^{2}-16}}{x}dx
integral of (sqrt(w))/(sqrt(1-\sqrt{w))}	\int\:\frac{\sqrt{w}}{\sqrt{1-\sqrt{w}}}dw
limit as x approaches 1 of 2/((x-1)^4)	\lim\:_{x\to\:1}(\frac{2}{(x-1)^{4}})
integral of u^{-1}	\int\:u^{-1}du
(\partial)/(\partial x)(3x^2+5y^7+9xy)	\frac{\partial\:}{\partial\:x}(3x^{2}+5y^{7}+9xy)
integral from 2 to 4 of (1-(x-3)^2)	\int\:_{2}^{4}(1-(x-3)^{2})dx
(\partial)/(\partial x)(sqrt(x+1))	\frac{\partial\:}{\partial\:x}(\sqrt{x+1})
integral from 1 to 4 of yln(y)	\int\:_{1}^{4}y\ln(y)dy
sum from n=0 to infinity of (e/2)^n	\sum\:_{n=0}^{\infty\:}(\frac{e}{2})^{n}
integral of xln(x+3)	\int\:x\ln(x+3)dx
integral from 1 to e of 8t^2ln(t)	\int\:_{1}^{e}8t^{2}\ln(t)dt
derivative of f(x)=sqrt(x^2+6x-1)	derivative\:f(x)=\sqrt{x^{2}+6x-1}
y^{'''}-y^{''}-y^'+y=5	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}-y^{\prime\:}+y=5
integral of 7cot^5(x)sin^4(x)	\int\:7\cot^{5}(x)\sin^{4}(x)dx
integral from 0 to 1 of (36)/((2x+1)^3)	\int\:_{0}^{1}\frac{36}{(2x+1)^{3}}dx
integral of 1/x+1/(x^2)+1/(x^3)	\int\:\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}dx
integral of sin(2x)sin(7x)	\int\:\sin(2x)\sin(7x)dx
(dy}{dx}=\frac{sin(x))/y ,y(0)=1	\frac{dy}{dx}=\frac{\sin(x)}{y},y(0)=1
(\partial)/(\partial x)(y*e^{-x})	\frac{\partial\:}{\partial\:x}(y\cdot\:e^{-x})
(3x^3)^'	(3x^{3})^{\prime\:}
integral of cot^4(x)csc^2(x)	\int\:\cot^{4}(x)\csc^{2}(x)dx
integral of-sin(x)+1/(cos^2(x))	\int\:-\sin(x)+\frac{1}{\cos^{2}(x)}dx
integral of x^2-ln(x^2)+k	\int\:x^{2}-\ln(x^{2})+kdx
integral from 1 to 5 of 1	\int\:_{1}^{5}1dx
integral of x^2*e^{-ax}	\int\:x^{2}\cdot\:e^{-ax}dx
taylor 1/((x-1))	taylor\:\frac{1}{(x-1)}
limit as x approaches 2 of ln(x/(x^2-4))	\lim\:_{x\to\:2}(\ln(\frac{x}{x^{2}-4}))
derivative of ay(e^{by})	derivative\:ay(e^{by})
derivative of ln(-x)	derivative\:\ln(-x)
integral of (12)/(x^{-1)+3}	\int\:\frac{12}{x^{-1}+3}dx
(dy)/(dx)=3+12x+9y+36xy	\frac{dy}{dx}=3+12x+9y+36xy
derivative of 1/(2x+9)	\frac{d}{dx}(\frac{1}{2x+9})
integral from 1 to 4 of (2x+1)	\int\:_{1}^{4}(2x+1)dx
(\partial)/(\partial x)((2s-3x)/(3s+5x))	\frac{\partial\:}{\partial\:x}(\frac{2s-3x}{3s+5x})
limit as x approaches-2 of sqrt(8+x^2)	\lim\:_{x\to\:-2}(\sqrt{8+x^{2}})
sum from n=1 to infinity of (-1/2)^n	\sum\:_{n=1}^{\infty\:}(-\frac{1}{2})^{n}
y^{''}-y^'-2y=8,y(0)=0,y^'(0)=5	y^{\prime\:\prime\:}-y^{\prime\:}-2y=8,y(0)=0,y^{\prime\:}(0)=5
limit as x approaches 3 of 4^{x^3}-8x	\lim\:_{x\to\:3}(4^{x^{3}}-8x)
limit as x approaches pi-of sin(x)	\lim\:_{x\to\:π-}(\sin(x))
(\partial)/(\partial x)(9-x^2-y^2)	\frac{\partial\:}{\partial\:x}(9-x^{2}-y^{2})
integral of (6x+2)/(3x^2+2x)	\int\:\frac{6x+2}{3x^{2}+2x}dx
integral from 0 to 1 of 1/(sqrt(3-x^2))	\int\:_{0}^{1}\frac{1}{\sqrt{3-x^{2}}}dx
integral of (x^6)/((4-x^7)^2)	\int\:\frac{x^{6}}{(4-x^{7})^{2}}dx
derivative of 7sec(xtan(x))	\frac{d}{dx}(7\sec(x)\tan(x))
integral from 2 to 4 of e^{3x-y}	\int\:_{2}^{4}e^{3x-y}dy
derivative of (3^{2/3}-x^{2/3}^{3/2})	\frac{d}{dx}((3^{\frac{2}{3}}-x^{\frac{2}{3}})^{\frac{3}{2}})
limit as x approaches 0 of (5x^2)/2	\lim\:_{x\to\:0}(\frac{5x^{2}}{2})
y^'+1/t y= 1/(t^2)	y^{\prime\:}+\frac{1}{t}y=\frac{1}{t^{2}}
f(x)=x^2cos(x)	f(x)=x^{2}\cos(x)
integral of e^{(-x/4)}	\int\:e^{(-\frac{x}{4})}dx
derivative of x^2+x-8	derivative\:x^{2}+x-8
integral of 7xarcsin(x)	\int\:7x\arcsin(x)dx
limit as x approaches 0 of 9/x-9/(\|x\|)	\lim\:_{x\to\:0}(\frac{9}{x}-\frac{9}{\left\|x\right\|})
integral of ((sin(ln(x))))/x	\int\:\frac{(\sin(\ln(x)))}{x}dx
4y^{''}+4y^'-3y=cos(2x)	4y^{\prime\:\prime\:}+4y^{\prime\:}-3y=\cos(2x)
integral from 2 to 3 of (26)/(sqrt(3-x))	\int\:_{2}^{3}\frac{26}{\sqrt{3-x}}dx
derivative of f(x)=(e^x)/(8x^2+3)	derivative\:f(x)=\frac{e^{x}}{8x^{2}+3}
sum from n=1 to infinity of (4^n)/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{4^{n}}{6^{n}}
integral of (((x)^2-5)^52x)	\int\:(((x)^{2}-5)^{5}2x)dx
limit as x approaches-1+of ln\|x+1\|	\lim\:_{x\to\:-1+}(\ln\left\|x+1\right\|)
derivative of x^2e^{(-x/(10)})	\frac{d}{dx}(x^{2}e^{\frac{-x}{10}})
tangent of f(x)= x/(x^2-15),\at x=4	tangent\:f(x)=\frac{x}{x^{2}-15},\at\:x=4
y^{''}+25y^'=0	y^{\prime\:\prime\:}+25y^{\prime\:}=0
derivative of f(x)=7e^{x^2-5x+6}	derivative\:f(x)=7e^{x^{2}-5x+6}
integral of (10x+4)sqrt(5x^2+4x)	\int\:(10x+4)\sqrt{5x^{2}+4x}dx
integral from 1 to 3 of ((ax)^3+e^{-bx})	\int\:_{1}^{3}((ax)^{3}+e^{-bx})dx
integral from 0 to 2 of 4x	\int\:_{0}^{2}4xdx
limit as x approaches 1 of sqrt(1-x)	\lim\:_{x\to\:1}(\sqrt{1-x})
simplify 1/2 \sqrt[3]{x}	simplify\:\frac{1}{2}\sqrt[3]{x}
y^{''}+16y=csc^2(4t)	y^{\prime\:\prime\:}+16y=\csc^{2}(4t)
integral from 1 to 9 of 2/(x^3)	\int\:_{1}^{9}\frac{2}{x^{3}}dx
integral of 1/((16t^2+9)^2)	\int\:\frac{1}{(16t^{2}+9)^{2}}dt
integral of-2e^{3x}+5/x	\int\:-2e^{3x}+\frac{5}{x}dx
limit as x approaches 0 of 18+(20)/(x^3)	\lim\:_{x\to\:0}(18+\frac{20}{x^{3}})
integral of 1/((4x+3)^2)	\int\:\frac{1}{(4x+3)^{2}}dx
integral of-xsin(z)	\int\:-x\sin(z)dz
integral of (2+x+x^2+3x^3)	\int\:(2+x+x^{2}+3x^{3})dx
derivative of (x+5/(x-3))	\frac{d}{dx}(\frac{x+5}{x-3})
d/(dy)(y^{4/5})	\frac{d}{dy}(y^{\frac{4}{5}})
y^'=y(xy^4+5)	y^{\prime\:}=y(xy^{4}+5)
integral from 1 to 7 of (x^2-4x-12)	\int\:_{1}^{7}(x^{2}-4x-12)dx
derivative of {f}(x(x)^{-1}(x^2))	\frac{d}{dx}({f}(x)(x)^{-1}(x^{2}))
integral of sin(x)*tan(x)	\int\:\sin(x)\cdot\:\tan(x)dx
integral from 0 to 1 of pi(5x^2)^2	\int\:_{0}^{1}π(5x^{2})^{2}dx
integral of x-csc(x)cot(x)	\int\:x-\csc(x)\cot(x)dx
integral of (sin(7x))	\int\:(\sin(7x))dx
derivative of 1/2 ln(2x)	\frac{d}{dx}(\frac{1}{2}\ln(2x))

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