7. Antiderivatives & Indefinite Integrals

Evaluate the indefinite integral as an infinite series: $\int arctan\left(x^4\right) dx$

Evaluate the indefinite integral as a power series: $\int \frac{1}{1-t^7} dt$.

Evaluate the indefinite integral. (Remember the constant of integration.) $\int ln\left(x\right) dx$

Evaluate the indefinite integral: $\int cos\left(6t\right) dt$

Evaluate the integral. (Use c for the constant of integration.) $\int wln\left(w\right)dw$

Find $f\(\left\)(x\(\right\))$ by evaluating the following indefinite integral.

$f\left(x\right)=\int (8x^7+10x-20)dx$

Evaluate the indefinite integral as an infinite series: ${\int }_{}^{}\left(\cos \right(x)-1)xdx$.

Find $f\(\left\)(x\(\right\))$ by evaluating the following indefinite integral.

$f\(\left\)(x\(\right\))=\(\int\[\left\)(100x^2-35x-\(\frac{13}{2}\]\right\))dx$

Evaluate the indefinite integral: ${4x}^2+5x+1 dx$

Evaluate the indefinite integral. (Use $c$ for the constant of integration.) $\int x(x^2+x+2)dx$

Evaluate the integral. (Use c for the constant of integration.) $\int 2{\sin }^2\left(x\right){\cos }^3\left(x\right)dx$

Evaluate the indefinite integral as a power series: $\int \frac{1}{1-t^9} dt$.

Evaluate the indefinite integral. (Use c for the constant of integration.)

$${\int }_{}^{}\frac{sin\left(t\right)}{1+cos\left(t\right)} dt$$

Evaluate the definite integral if it exists: ${\int }_1^3{x}^2+2x+4 dx$

Evaluate the indefinite integral: ${\int }_{}^{}{x}^{2}dx$