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Popular Calculus Problems

integral of 4cos(sqrt(x))	\int\:4\cos(\sqrt{x})dx
derivative of f(x)=x^{3/2}+1/(x^{5/2)}	derivative\:f(x)=x^{\frac{3}{2}}+\frac{1}{x^{\frac{5}{2}}}
derivative of x^2e^{7x}	\frac{d}{dx}(x^{2}e^{7x})
integral of ((e^t+2e^{2t}))/(e^{3t)}	\int\:\frac{(e^{t}+2e^{2t})}{e^{3t}}dt
(\partial)/(\partial x)(u/x)	\frac{\partial\:}{\partial\:x}(\frac{u}{x})
integral from-1 to 1 of 2sqrt(1-(x^2)/2)	\int\:_{-1}^{1}2\sqrt{1-\frac{x^{2}}{2}}dx
tangent of (12x)/(x^6)	tangent\:\frac{12x}{x^{6}}
limit as x approaches 1 of ln(x^2)	\lim\:_{x\to\:1}(\ln(x^{2}))
f(x)=sin^4(3x+5)	f(x)=\sin^{4}(3x+5)
limit as x approaches 0 of 3xcsc(5x)	\lim\:_{x\to\:0}(3x\csc(5x))
derivative of f(x)=cos(x)-9x	derivative\:f(x)=\cos(x)-9x
derivative of sin(cos(sin(x)))	\frac{d}{dx}(\sin(\cos(\sin(x))))
(\partial)/(\partial x)(c/x)	\frac{\partial\:}{\partial\:x}(\frac{c}{x})
integral of 3x^2-cos(x)+C	\int\:3x^{2}-\cos(x)+Cdx
integral of x/(2021^x)	\int\:\frac{x}{2021^{x}}dx
derivative of x^{11}h(x)	\frac{d}{dx}(x^{11}h(x))
expand-(2x)/((x^2+4)^2)	expand\:-\frac{2x}{(x^{2}+4)^{2}}
tangent of f(x)= 8/x	tangent\:f(x)=\frac{8}{x}
limit as x approaches-pi of (x+pi)cot(x)	\lim\:_{x\to\:-π}((x+π)\cot(x))
integral of sin^7(y)	\int\:\sin^{7}(y)dy
integral of 3/35 x^2	\int\:\frac{3}{35}x^{2}dx
y^{'''}+2y^{''}-13y^'+10y=0	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}-13y^{\prime\:}+10y=0
y^{''}+2y^'+4y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+4y=0
integral of 7/(sqrt(1+x^2))	\int\:\frac{7}{\sqrt{1+x^{2}}}dx
derivative of x^2ln(7x)	derivative\:x^{2}\ln(7x)
tangent of f(x)=sqrt(x+1),\at x=8	tangent\:f(x)=\sqrt{x+1},\at\:x=8
integral of (x^2+2x)^3	\int\:(x^{2}+2x)^{3}dx
derivative of tsin(t)	derivative\:t\sin(t)
derivative of 2/((3x^2+7^2))	\frac{d}{dx}(\frac{2}{(3x^{2}+7)^{2}})
(\partial)/(\partial x)(e^{xy}sin(z))	\frac{\partial\:}{\partial\:x}(e^{xy}\sin(z))
derivative of 4x^{2x}	\frac{d}{dx}(4x^{2x})
integral from 1 to 2 of (x^2+1)	\int\:_{1}^{2}(x^{2}+1)dx
integral of (2x)/((1+x)^2)	\int\:\frac{2x}{(1+x)^{2}}dx
integral of 3/(t^2)	\int\:\frac{3}{t^{2}}dt
(\partial)/(\partial x)(sec^5(x^3y^3))	\frac{\partial\:}{\partial\:x}(\sec^{5}(x^{3}y^{3}))
derivative of asin(x)+bcos(x)	derivative\:a\sin(x)+b\cos(x)
derivative of f(x)=x+1+1/(x^2)	derivative\:f(x)=x+1+\frac{1}{x^{2}}
derivative of tan^3(2x)	\frac{d}{dx}(\tan^{3}(2x))
integral of 7/(2x^{9/4)}	\int\:\frac{7}{2x^{\frac{9}{4}}}dx
y^{''}-8y^'+16y=t^{-9}e^{4t}	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=t^{-9}e^{4t}
limit as n approaches infinity of n/6	\lim\:_{n\to\:\infty\:}(\frac{n}{6})
(\partial)/(\partial y)(ye^{xy}+2x-1)	\frac{\partial\:}{\partial\:y}(ye^{xy}+2x-1)
(\partial)/(\partial x)(8y-4x)	\frac{\partial\:}{\partial\:x}(8y-4x)
(\sqrt[3]{x})^'	(\sqrt[3]{x})^{\prime\:}
y^{''}-6y^'+34y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+34y=0
(\partial)/(\partial x)(1/3 x^3)	\frac{\partial\:}{\partial\:x}(\frac{1}{3}x^{3})
integral from-1 to 2 of (7-3t)	\int\:_{-1}^{2}(7-3t)dt
integral of csc(x	\int\:\csc(d)xdx
slope ofintercept (-7,-3),(-5,-8)	slopeintercept\:(-7,-3),(-5,-8)
integral of sin^4(θ)cos^2(θ)	\int\:\sin^{4}(θ)\cos^{2}(θ)dθ
integral from 1 to 7 of x^2ln(x)	\int\:_{1}^{7}x^{2}\ln(x)dx
tangent of 2-x^2	tangent\:2-x^{2}
d/(dt)(acos(w(t)t)+bsin(w(t)t))	\frac{d}{dt}(a\cos(w(t)t)+b\sin(w(t)t))
derivative of ln(sqrt((x^3/(x^5+1))))	\frac{d}{dx}(\ln(\sqrt{\frac{x^{3}}{x^{5}+1}}))
derivative of y=sqrt(10+tan^2(x))	derivative\:y=\sqrt{10+\tan^{2}(x)}
integral of (sqrt(cot(β)))/(sin^6(β))	\int\:\frac{\sqrt{\cot(β)}}{\sin^{6}(β)}dβ
integral of 1/(1+1/x)	\int\:\frac{1}{1+\frac{1}{x}}dx
derivative of 4sqrt(x+2)	\frac{d}{dx}(4\sqrt{x+2})
derivative of 8/(3+x^2)	\frac{d}{dx}(\frac{8}{3+x^{2}})
integral of x^{1/2}	\int\:x^{\frac{1}{2}}dx
derivative of (y-2x/(2y-x))	\frac{d}{dx}(\frac{y-2x}{2y-x})
maclaurin 1/(1+2x)	maclaurin\:\frac{1}{1+2x}
integral of (x^3-1)/x	\int\:\frac{x^{3}-1}{x}dx
(dy)/(dx)=21x^2e^{-y}	\frac{dy}{dx}=21x^{2}e^{-y}
area x+y=2,x=y^2-2y	area\:x+y=2,x=y^{2}-2y
derivative of ((x^2-5^3)/(125))	\frac{d}{dx}(\frac{(x^{2}-5)^{3}}{125})
limit as x approaches infinity of k/x	\lim\:_{x\to\:\infty\:}(\frac{k}{x})
integral of (x)^{3/2}	\int\:(x)^{\frac{3}{2}}dx
y^{''}+y=csc^2(x)	y^{\prime\:\prime\:}+y=\csc^{2}(x)
integral of x(x^2+1)^4	\int\:x(x^{2}+1)^{4}dx
derivative of e^x-4x^3	derivative\:e^{x}-4x^{3}
derivative of (sqrt(x-1)/(sqrt(x+1)))	\frac{d}{dx}(\frac{\sqrt{x-1}}{\sqrt{x+1}})
(\partial)/(\partial x)(1/2 ln(x+y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}\ln(x+y))
y^{''}+k^2y=0	y^{\prime\:\prime\:}+k^{2}y=0
derivative of (x+2^2)	\frac{d}{dx}((x+2)^{2})
integral of 1/(5x-3)	\int\:\frac{1}{5x-3}dx
integral of sec^4(5x)tan^6(5x)	\int\:\sec^{4}(5x)\tan^{6}(5x)dx
derivative of (ln(1+x))/(1-x)	derivative\:\frac{\ln(1+x)}{1-x}
x^2-y^2+xy(dy)/(dx)=0	x^{2}-y^{2}+xy\frac{dy}{dx}=0
integral of (3x)/((6-x^2)^3)	\int\:\frac{3x}{(6-x^{2})^{3}}dx
integral of ((ln(x))^2+1)/(xln(x))	\int\:\frac{(\ln(x))^{2}+1}{x\ln(x)}dx
(d^2)/(dt^2)(cos^2(t))	\frac{d^{2}}{dt^{2}}(\cos^{2}(t))
derivative of (ln(3x)/(sqrt(x)))	\frac{d}{dx}(\frac{\ln(3x)}{\sqrt{x}})
3y^{''}+13y^'+4=0,y(0)=0,y^'(0)=0	3y^{\prime\:\prime\:}+13y^{\prime\:}+4=0,y(0)=0,y^{\prime\:}(0)=0
derivative of 3(7-3x^3^3)	\frac{d}{dx}(3(7-3x^{3})^{3})
-(1+y^2)^{1/2}dx+4xydy=0	-(1+y^{2})^{\frac{1}{2}}dx+4xydy=0
derivative of 1+csc(x)	\frac{d}{dx}(1+\csc(x))
limit as x approaches-infinity of-xe^x	\lim\:_{x\to\:-\infty\:}(-xe^{x})
area y=x^2-4x,y=2x-x^2	area\:y=x^{2}-4x,y=2x-x^{2}
tangent of f(x)=x+1/x ,\at x=3	tangent\:f(x)=x+\frac{1}{x},\at\:x=3
derivative of (4x^2+1)/(x^2+5)	derivative\:\frac{4x^{2}+1}{x^{2}+5}
derivative of x^4-6x^2+4	\frac{d}{dx}(x^{4}-6x^{2}+4)
derivative of xe^{1/x}	derivative\:xe^{\frac{1}{x}}
derivative of 1+4x^{3/2}	\frac{d}{dx}(1+4x^{\frac{3}{2}})
integral of (2w)/2	\int\:\frac{d^{2}w}{2}dx
f(t)=ln(t+1)	f(t)=\ln(t+1)
derivative of x^2+3x+sqrt(4)	\frac{d}{dx}(x^{2}+3x+\sqrt{4})
t*(dy)/(dt)+37y= 1/t	t\cdot\:\frac{dy}{dt}+37y=\frac{1}{t}
slope of x^2-1	slope\:x^{2}-1
integral of 1/(y-4)	\int\:\frac{1}{y-4}dy

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