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Practice: Parts with Poly and Trig & Substitution

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Wize University Calculus 1 Textbook > Integration Techniques

Integration by Parts

6 Activities

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Q:\textbf{Q:} Integrate ∫x3 cos⁡(x2−1)dx\displaystyle\int_{ }^{ }x^3\ \cos\left(x^2-1\right)dx

More Integration by Parts Questions:
Find ∫1ex2ln⁡ x dx\displaystyle\int_1^ex^2\ln\ x\ dx
Integration by Parts
Evaluate ∫x2sin⁡(πx)dx\displaystyle\int x^2 \sin(\pi x) dx
Integration by Parts
Evaluate ∫x2sin⁡(πx)dx\displaystyle\int x^2 \sin(\pi x) dx
Integration by parts
Evaluate
∫xsin⁡x dx\int x\sin x\ dx
Find ∫1ex2ln⁡ x dx\displaystyle\int_1^ex^2\ln\ x\ dx
Practice Question: I by P *
Practice Question
Evaluate∫sec⁡3x   ⁣dx{\displaystyle\int}\sec^3x \space\de{x}.
Practice Question: I by P
Practice Question
Evaluate ∫xsec⁡xtan⁡x  ⁣dx{\displaystyle\int}x\sec x\tan x\de{x}.
Integration by parts
Evaluate
∫xsin⁡x dx\int x\sin x\ dx
Integration by Parts
Evaluate ∫x2sin⁡(πx)dx\displaystyle\int x^2 \sin(\pi x) dx
Integration by parts
Evaluate
∫xsin⁡x dx\int x\sin x\ dx
Integration by parts
Evaluate
∫xsin⁡x dx\int x\sin x\ dx
Integration by Parts
Evaluate
∫x2cos⁡(x) dx\int x ^2\cos (x) \ dx
Integration by parts
Evaluate
∫xsin⁡x dx\int x\sin x\ dx
Integration by Parts
Evaluate ∫x2sin⁡(πx)dx\displaystyle\int x^2 \sin(\pi x) dx
Evaluate the integral ∫−11x2ex  ⁣dx{\displaystyle\int^1_{-1}}x^2e^x\de{x}.
Evaluate the integral ∫(2x+1)cos⁡(x/2)  ⁣dx\displaystyle\int_{ }^{ }(2x+1)\cos(x/2)\de{x}.
Integration by Parts
Evaluate
∫x2cos⁡(x) dx\int x ^2\cos (x) \ dx
Integration by parts
Evaluate
∫xsin⁡x dx\int x\sin x\ dx
Practice: Secant with Parts
Q:\textbf{Q:} Evaluate ∫sec⁡3x dx\displaystyle\int\sec^3 x\ dx
Find ∫1ex2ln⁡ x dx\displaystyle\int_1^ex^2\ln\ x\ dx
Find∫xcos⁡(2−3x) dx\displaystyle\int_{ }^{ }x\cos\left(2-3x\right)\ dx
Parts with Exp and Trig, going Round
Integrate ∫e3xcos⁡(5x)dx\displaystyle \int e^{3x}\cos(5x)dx
Practice: Parts with Poly and Trig, Twice
Q:\textbf{Q:} Integrate∫x2 cos⁡ x dx\displaystyle\int_{ }^{ }x^2\ \cos\ x\ dx
Evaluate the integral ∫(2x+1)cos⁡(x/2)  ⁣dx\displaystyle\int_{ }^{ }(2x+1)\cos(x/2)\de{x}.
(a) 4(2x+1)sin⁡(x/2)+2cos⁡(x/2)+C4(2x+1)\sin(x/2)+2\cos(x/2)+C (b) 4(2x+1)sin⁡(x/2)+8cos⁡(x/2)+C4(2x+1)\sin(x/2)+8\cos(x/2)+C
(c) 2(2x+1)sin⁡(x/2)+2cos⁡(x/2)+C2(2x+1)\sin(x/2)+2\cos(x/2)+C (d) 2(2x+1)sin⁡(x/2)+8cos⁡(x/2)+C2(2x+1)\sin(x/2)+8\cos(x/2)+C
Find ∫1ex2ln⁡ x dx\displaystyle\int_1^ex^2\ln\ x\ dx
Practice Question
Practice Question
Evaluate ∫xsec⁡xtan⁡x  ⁣dx{\displaystyle\int}x\sec x\tan x\de{x}.
Practice Question: I by P *
Practice Question
Evaluate∫sec⁡3x   ⁣dx{\displaystyle\int}\sec^3x \space\de{x}.
Practice Question: I by P
Practice Question
Evaluate ∫xsec⁡xtan⁡x  ⁣dx{\displaystyle\int}x\sec x\tan x\de{x}.
Evaluate the integral ∫−11x2ex  ⁣dx{\displaystyle\int^1_{-1}}x^2e^x\de{x}.
Practice Question
Practice Question
Evaluate ∫xsec⁡xtan⁡x  ⁣dx{\displaystyle\int}x\sec x\tan x\de{x}.
Evaluate the integral ∫(2x+1)cos⁡(x/2)  ⁣dx\displaystyle\int_{ }^{ }(2x+1)\cos(x/2)\de{x}.
Evaluate the integral ∫−11x2ex  ⁣dx{\displaystyle\int^1_{-1}}x^2e^x\de{x}.
Integration by Parts
Evaluate ∫x2sin⁡(πx)dx\displaystyle\int x^2 \sin(\pi x) dx
Integration by parts
Find
∫cos⁡2xdx\int \cos^2 x dx
Integration Medley
Practice Question
Evauate ∫arctan⁡(x)  ⁣dx{\displaystyle\int}\arctan(\sqrt{x})\de{x}.
Evaluate∫(xln⁡x)2dx\int_{ }^{ }\left(x\ln x\right)^2dx
Practice Question: I by P *
Practice Question
Evaluate∫sec⁡3x   ⁣dx{\displaystyle\int}\sec^3x \space\de{x}.
Practice Question: I by P
Practice Question
Evaluate ∫xsec⁡xtan⁡x  ⁣dx{\displaystyle\int}x\sec x\tan x\de{x}.
Practice Question: I by P
Practice Question
Find ∫xarctan⁡x  ⁣dx{\displaystyle \int}x\arctan x\de{x}.
Integration by Parts
Evaluate
∫x2cos⁡(x) dx\int x ^2\cos (x) \ dx
Evaluate ∫x2e−xdx\displaystyle\int x^2e^{-x}dx
Integration by parts
Evaluate
∫xsin⁡x dx\int x\sin x\ dx
Practice Question: I by P
Evaluate ∫xsec⁡xtan⁡x  ⁣dx{\displaystyle\int}x\sec x\tan x\de{x}.
Find ∫π2π xcos⁡ x dx\displaystyle\int_{\frac{\pi}{2}}^{\pi}\ x\cos\ x\ dx
Find∫ex sin⁡(3x)dx\displaystyle\int e^x\ \sin\left(3x\right)dx
Find ∫1ex2ln⁡ x dx\displaystyle\int_1^ex^2\ln\ x\ dx
Find∫xcos⁡(2−3x) dx\displaystyle\int_{ }^{ }x\cos\left(2-3x\right)\ dx
Practice: Secant with Parts
Q:\textbf{Q:} Evaluate ∫sec⁡3x dx\displaystyle\int\sec^3 x\ dx
Parts with Exp and Trig, going Round
Integrate ∫e3xcos⁡(5x)dx\displaystyle \int e^{3x}\cos(5x)dx
Practice: Parts with Poly and Trig, Twice
Q:\textbf{Q:} Integrate∫x2 cos⁡ x dx\displaystyle\int_{ }^{ }x^2\ \cos\ x\ dx
Practice: Parts with Poly and Trig & Substitution
Q:\textbf{Q:} Integrate ∫x3 cos⁡(x2−1)dx\displaystyle\int_{ }^{ }x^3\ \cos\left(x^2-1\right)dx